I noticed that for quite some time no games would show as "updated" in my library on the GOG homepage. I check there on a regular base to download the offline installers. I wasn't really bothered even if it seemed longer than usual since I got my last notification.

But today ... two of my games were updated through GOG galaxy ... nothing unusual, the offline installers come with some delay from time to time. Just for the sake of it, I then checked the homepage: New offline installers were avaiable.
But there was no notification about it.

Has this feature been removed together with the GOG downloader?

Do we HAVE to start Galaxy now to see if a game was updated?

It's very annoying for us Non-Galaxy users isn't it?

Personally I refuse to use Galaxy let alone be strong-armed into using Galaxy by what I believe is intentional inconvenience of non-Galaxy customers. The best way imo to see if a game was actually updated for offline installer use (which the blue dots did not always accurately reflect in my experience), is to rely on other users. My recommendation is to read this topic often: https://www.gog.com/forum/general/the_what_did_just_update_thread

In that topic, make sure to look at when people say the "standalone" installers have been updated, those are the ones I assume you are looking for if you are downloading them through the browser and choosing "Offline Backup Installers". In other words, Galaxy gets updates first while us second-class browser downloader citizens have to wait days and sometimes even longer if we want to get the complete installers outside of using Galaxy.

If you also wish they would bring the Downloader back, you're not alone. There are 913 wishlist votes at the time of me writing this and the votes keep growing everyday. https://www.gog.com/wishlist/site/keep_the_gog_downloader_and_keep_it_up_to_date

My Windows cannot access the internet, so Galaxy is no option for me. Im using an Ubuntu in a VirtualBox to access internet (aka "download offline installer").
So Galaxy wouldn't even be an option for me. And yes: it's extremely annoying

Especially when you miss a 50mb patch and you have to download the whole 15 GB game again, because older patches get removed.

Guess I'll ask the support via ticket on a weekly basis to send me a list of the games I own and that were updated in the last week...

There are several threads on this topic. Try mine for instance in which there are linked threads and wishlist entries, plus I put in a ticket about it:
https://www.gog.com/forum/general/provide_a_full_and_complete_changelogged_download_system