The first one yes. Minor stuff though, something to put on the Todo list :)

About the persistence idk. The more the better I guess but not that important I think.

One more reaction: I have a few of these type of enrichments on my roadmap, where I'm pretty certain I can do them in a reasonable amount of time (installer size, 'cosmetics'), and a whole bunch more on my personal investigation list. I have a decent infrastructure for churning through such things reasonably swiftly (having already done release dates and categorization/grouping (demo, goodie, etc)). Feel free to mention any specific other enrichments you'd love to see - I'm always interested in what people care about in this space.

I did not even consider gogsieve; GOG seems pretty relaxed about using their name in projects like gogdb, but I tend to err on the cautious side, and so deliberately picked a generic name. Plus, this way I keep the option open to expand beyond GOG if I ever achieve that perfection-incarnate state. :P

Thanks. Added this to the roadmap.

Fixed. On the way there, I went down another rabbit hole and redid the way I'm scoring documents at the top level, which then necessitated tuning everything anew, but that has the added benefit that there's no longer an inherent scoring-boost for games with grouped products. (Before I was suppressing that through weighting on the children; now I'm taking the max score from grouped products, irrespective of if they're the parent or a child.)

Sorry for the silence... I rather... chickened away. When it became clear just how much work you're putting into it and at what rate, comments didn't seem like something that could be gathered at a glance and thrown here among many (in part because there aren't many to begin with), but something that should be taken way more seriously and with more responsibility than I feel I can manage and, yeah, like I said, I was slinking away...

Also, I'm with HunchBluntley here in the sense that your site seems aimed at those looking for things to buy, not those looking for information about the titles and better ways to search and sort the GOG catalog as a general purpose matter, so my interest are also features that'd be at home in GOGDB instead of here.

But, yeah, in my case the "expert mode" for filters would be the top request.
Then import, whether manually (like MaGOG did it, so GOG API access or user privacy settings wouldn't matter) or automatically, and, in case of public ones, automatically sync wishlisted and owned titles, which would then also allow implemented the filters that also exist on GOG, exclude owned, list only wishlisted, include only DLCs for owned titles. And it'd also allow another thing that existed on MaGOG, searching user wishlists, which led to the nomination drives in the Community GA back in the day.
And then what I've said before, have a way to make sure that the include NSFW setting won't be cleared no matter what you do on the site. And yeah, that should also go for the selected country for prices, and for the sorting option.
But the bigger thing would be for filters in general to be preserved between searches, as in be able to change the keywords but keep the filters. Otherwise it's a royal pain to use, and would still be so even with "expert mode". I mean, the NSFW setting, country and sorting are things that really should be kept for the user at all times, but those are one click each, while if you set up some complex filtering that you're looking for, that may mean dozens of selections, and needing to do them again every single time if you want to search for who knows how many things, well, it's not going to happen, might as well deal with GOG's search instead.
As for searching, I want it to be exact, not try to determine what I mean or list things that don't include the exact keywords I entered. Otherwise, see little point in it.

Oh yeah, I can be rather... intense, when focusing on something. Thanks for returning and explaining!

I think what's at play here is that I can more easily envision the needs of people who're looking for a next game, and have strived for feature parity with GOG (which obviously is set up for selling things), but then "better". I do want the search to be very general purpose, and usable for a wide range of usecases - but I might need a bit more help to understand what that'd entail. Give me examples of what you'd be searching for, really spell them out? (And my innate reaction then will be to dissect that and maybe argue why it wouldn't be possible or feasible or clashing with other things - but that's just my process for coming to grips with it, while in the back of my mind I'll be mulling over possibilities until I come up with a "what if I did ..." that seems doable.)

So in a top 3, this would be #1, with expert mode on #2 and import on #3?

Workaround for now: edit just the query in the URL. (I've deliberately made the URL as readable as possible, so you can understand what each part does.)

I'm gaming out various ways to make this work in the UI; this is just spitballing for now, but I might go for a checkbox when any non-default filters are present, to search again with that selection. Or maybe a toggle in the sidebar to always do that. Or showing the search terms "as" as applied filter, but then with editing possibility.

My main issue is that if you apply filters before you search, you have a high chance of getting back zero results, and I don't think there's any way I can indicate which filters are the specific cause. Again, better understanding of which types of searches and filters you'd specifically want to try, might help me realize that this is not actually a problem, and/or figure out workarounds for such.

So these are things about the current search that are non-exact:
1) stemming. If you search for "adventures", you'll also get back results for "adventurer", "adventure", "adventuring", etc. This is very useful when you're searching for either a specific game you don't know the title of, or for any game with certain characteristics - but I know it's not useful when you search for the title of a specific game - which is why I search through titles three times, once with a very high weight for exact match, then with a lower weight for a stemming match, and finally with an even lower weight for a typod match.
2) typos and transliteration. If you search for "eternak", you'll get results for "eterna", "eternal", etc; if you search for "mobius", you'll also get results for "moebius" and "möbius". It means that if you search for "Ys", you also get results for "golf vs zombies" (due to "vs" being 1 letter difference from "ys"). Ah! I wanted to write that this is "solved" by proper weighting, but as I was typing this, I realized that this makes sorting less useful! (Also for my previous point.) That needs pondering... What you can do to prevent this, is to put such words either in a phrase - "ys" - or with a + in front of it - +ys - both will prevent the "fuzzy" search (though not the stemming).
3) not requiring all words/phrases. Only 75% of your search words/phrases are required, rounded up; so if you enter 4 words, each result will match at least 3. If you don't want this behaviour, you can put a + in front of each word/phrase you want to require in every result.
4) synonyms. There aren't all that many, but 40k will match 40,000, rpg will match roleplaying game and so on.

(Wanted to write more, but need to be busy irl for a bit now.)

Well, these wouldn't so much be useful to me specifically as I could see them being useful to plenty of others -- "games that run in ScummVM", "console game ROMs running in an emulator"/"games with an extractable ROM"...and I actually can't remember what other examples I had in mind before. Some of the others were more things that would be better suited to store tags, or to something like a GOGMix -- e.g., "games based on properties from other media".
Also, similar to being able to search by the names of individual games included in bundles, but also something that would require prior enrichment to work (which it seems you might've already implemented to at least some extent), is being able to search by alternative titles for games that were originally released under different names in different markets or at different times. However, this one is also not as necessary as it would've been if Gamesieve's search routine were more basic, as many of the titles of such games on GOG have at least some words in common between the different names (searching "thief the dark project" would bring up Thief™ Gold anyway because of "thief"), and some were re-released with amalgamated titles (like Fahrenheit: Indigo Prophecy Remastered) which include much or all of the different names. The only definite example of "search term with 0% overlap with the store title of a game it should return" that I could think of to test last night (or, indeed, right now) was searching "the dark project" and finding that it already returns Thief™ Gold.

[continued] ...I wonder if it's actually any of those four types of inexactness that's bothersome for you, or if it's more that I search in the complete text of product descriptions (as well as the names of goodies, developers and publishers)? This is what makes "the dark project" return "Thief Gold" (as HunchBluntley mentioned), but for the title of any game which contains generic words, it also returns a very long tail of games which happen to match the individual words somewhere. E.g. star trek return KCD2 as its very last result, as its soundtrack has tracks "The Trek" and "Beneath the Stars". Searching for "star trek" improves things marginally, but it still returns games which reference "star trek" in their descriptions.

...so yeah, help me fully understand your usecase(s)? Then I can determine what tweaks I'd need to make or what options I'd need to provide to make it possible.

In terms of priority, no, expert mode is #1, import #2, exact search #3, because as you say, there is a workaround for preserving filters. Shouldn't be needed, but it's there.
And searching everywhere shouldn't be the default I'd say, as for those ways to type a search to force it to be exact, they really should be spelled out there, so everyone'd have the "cheat sheet" in front of them when they search. Because as it is it's just a mess. If I want to look for a game on GOGDB I tend to search for a more unusual word or two from its title if they exist, or paste the whole thing if it's common, or on the other hand use the common part if I'm looking for a series, and usually get what I want, not a whole pile of unrelated results along with it.

Oh, but I'm adding something. Not on your roadmap, but listing the pricing matrix for a title, as in show prices in all regions covered, not just one, maybe have that as a toggle there next to the country selection. And of course list that in USD, to allow comparison. Something sorely missing since MaGOG poofed.

Otherwise, my use cases aren't for making purchases. If wishlist import would exist, it'd be nice to see at a glance whether the current discount for any wishlisted titles is the best ever. And any wishlist check means sort by title to be able to go through it in the same order, not move up and down for each title according to different sorting criteria.
But, anyway, my use cases would be things like looking for catalog additions within a certain period with certain release dates, like to see old vs. new games, or see which games were added in a month (so exact date needed) or a year, possibly adding certain genres or certain tags (inadequacy of the system notwithstanding) as filters. So basically the one thing that an external system would be useful for from that point of view would be the filtering by addition date (again, exact date, not just year), because otherwise GOG's search offers the options.

I finally thought of/remembered a couple more to try: "[the] stygian abyss" and "labyrinth of worlds" would each, ideally, return the Ultima™ Underworld 1+2 package (those phrases being the two games' respective subtitles), but neither did. (Though "labyrinth of worlds" -- without the quotation marks -- returns, among other things, every single one of the individual "games" "developed" by Whale Rock Games, for some reason.)

One field I would particularly like to be able to search to the exclusion of other fields would be companies ("dev/pub"). It's annoying to search for games from a certain company on the GOG site itself, because if you search for one of these names using the quick search (in the menu bar), the dropdown results show these company names, but will be limited to a certain number of product matches -- and, of course, there's no way to specify that it should only search in this field, so other stuff is possible to be returned as well. (Also, these quick results don't distinguish where the developers end and the publishers begin when there are more than two companies credited -- they're separated by commas all the same.) Meanwhile, doing the same search on GOG's main catalogue search page will show all matches, but not give you any way to see these company names at all without clicking through to each individual product page...and there's still no way to search or filter only by company.
Gamesieve is already better at this overall -- separating multiple co-developers or co-publishers with a comma, but developers from publishers with a slash within any displayed product result was a very welcome nuance -- but it would still be nice to be able to do a proper limited search, rather than having to filter down the results of an (often) otherwise-overly-broad pool after the fact.

Always good to see when things like that are noticed, as it's very deliberate! :)
What's annoying here is that GOG puts the company names as a single comma-separated field in the API (rather than as an array of names as was clearly intended), so I already need heuristics to split those up properly without "Inc." becoming the most popular developer and publisher of them all - but then there are exceptions like the developer "Capcom / GOG" where it's split with a slash, so Resident Evil and Dino Crises currently show as "Capcom / GOG / Capcom" rather than Capcom, GOG / Capcom. (That's on my list to fix next week.)

I've encountered this specific desire myself. My current workaround is indeed to filter on the developer/publisher after the search (since the search tends to be needed to make the developer/publisher show up in the filter; there are simply too many to list them all), but it's one of the prime candidates I'm keeping in mind for the possibility of doing field-specific searches (together with title).

This is not going to change. My vision of the site had two primary usecases:
1) "Show me specific game X, so I can see if it's current discount is a good one." This is basically what's offered by every price tracker out there, so not worthwhile in itself, even if me doing it for many currencies makes it slightly better.
2) "Show me all games in genre/niche Y, so I can see if there are any which I was previously unaware of but should investigate." This (particularly bubbling up new titles every week due to varying discounts) is where gamesieve is unique, offering something which the various price trackers and the like don't offer. It's also how I see it actively being used.

The second usecase requires searching through tags and descriptions, while it's helpful for the former. I'm primarily aiming to be a GOG search engine, not a GOG database explorer. (But the fact that there's active interest in a GOG database explorer, which I might be able to also cater to, is worthwhile! Just need to come to grips with what this'd entail.)

From my point of view, these ("phrases", -exclusions and +requires) are the most basic search engine operations, available pretty much anywhere, and something which people would try automatically. Are you simply not expecting them for gamesieve, or are they also unknown in other contexts, and do I need to adjust my expectations of what people are familiar with?

Still mulling over the rest of what you wrote. It already gave me some new clarity, but I might come back later with some followup questions.