I was playing Hexen for the first time in 25 years, give or take, and it just looked too dark. I thought maybe it was just nostalgia but I went and looked at YouTube playthroughs and the screenshots on GOG and they just look better. Still very pixelated, don't get me wrong, but significantly more solid. Does anyone else have this problem? Are there any solutions to boost the graphics quality?

I wanted to show a screenshot but it just shows the DosBox interface (Option 1 2 or 3 to launch the game) when I use print screen in game.

Hardly anyone uses DOSBox for Doom Engine games these days when a much better source port exists.

1. Download and unzip GZDoom https://zdoom.org/downloads
2. Copy your Hexen WAD files (HEXEN.WAD and HEXDD.WAD) into it.
3. Download and add the Hexen HD texture pack (neural upscaled textures that closely retain the look and style of the original).

and it will look and play far better.

Awesome! Thank you. So instead of using the GOG launcher, follow these instructions and launch through GZDoom?

Yes. It works exactly the same way for all the other Doom Engine games (Doom 1-2, Heretic, Strife, etc). You can still use community WADs with it too.

Excellent. Thank you very much for enlightening me about this.

Yeah. Nostalgia often prevents us from remembering how low resolution games used to be. But luckily, source ports are here to help.

As suggested, you can use GZDoom or one of the others. If you are after accuracy, Chocolate Hexen is the better choice:
https://www.chocolate-doom.org/wiki/index.php/Downloads

Much harder to set up than GZDoom though, so your choice.