In its store page, it says the game supports them, it even shows after the description. But in the GOG Launcher they don't show up, as if the game doesn't support them. Can this be fixed with an update?

Why do people search drm-free release on gog just to use a stupid launcher... I just don't get it.

I haven't played it that much so I haven't unlocked any achievements yet but good to know. Hopefully it gets patched soon.

I've played it just long enough to get one achievement to confirm it :D
This seems to be a recurring issue with devs/publishers leaving the achievements setting in "dev mode" which makes the list invisible.
Possibly a communication issue on GOG's side

Achievements are now visible normally! Thanks GOG!

Yep, achievements are loading now. All is good is the world again!