When we take a picture, it (supposedly) goes into a folder - but when I try to find the folder - there never seem to be any pictures in it... Is there a different location we need to go to to access those pictures when we use GOG?

Galaxy stores screenshots in "Documents\GOG Galaxy\Screenshots\No Man's Sky"

Photo mode in NMS itself stores screenshots in "Pictures\No Mans Sky"

If for some reason they are not saved in any of these folders check that your antivirus does not block access to these folders from the game. I had this happen yesterday, Bitdefenders "Safe files" feature was blocking NMS from saving screenshots.

Windows defender in Windows 10 also has a feature like this, but I don't think it is on by default.

Avast antivirus was blocking the screenshots here, both the Photo Mode and the F12 "live action" screenshots.

I kicked Avast to the curb for another reason and was surprised to notice that screenshots were being saved again. Some of the base Overseer's quests are like "take a picture of a desert planet" and they were on the drive.

So, mmodri's advice is sound. Check your antivirus.

While to some this might be obvious, to me in the beginning it wasn't: Galaxy will open the folder it saves screenshots to, if I choose "More -> Manage Installation -> Show Screenshots".

I'm aware, that this doesn't help with the problem at hand, but wanted to mention that there's a 'default' way to have that folder displayed other than navigating manually to it.