I have a problem, as pretty recently, I had Darkest Dungeon on GoG, but for some reason it refuses to launch, and instead goes briefly into sync before doing absolutely nothing. If anyone here knows how to fix the problem, please let me know, it would really help me out a lot.

Same. Tried to play again 2 days ago after a long (5-year) break. Had trouble but got it to start after 4 tries. Today nothing. From GOG it won't start at all. From desktop it crashes out when loading the savegame.

Edit: Seems to be related to a recent update? I tried reverting to the previous version (from 6 years ago rather than 1 month ago) and then turning off automatic update - I can now load and play my old save.

Same. I don't know what happen.

I had a similar problem.
If Cloud-Syncing is turned off and you have configured the starting executable (Manage Installation=>Features=>Launch Parameters) then GOG Galaxy tries to sync and fails despite Cloud being turned off. So the game is not started at all.

Using the standard settings (untick Launch Parameters) or the additional executable works normally.

Hope that solves your problem.