I haven't managed to find an answer on this. I have purchased some old games from GOG that I can't get to run under Windows but which work perfectly fine under Linux using Wine or Proton. However, I have not seen a way to actually get the GOG launcher to run with the game, detect it, and manage cloud saving and playtime tracking.

I know there are manual cloud saving solutions however I would highly prefer to use GOG's own service, especially since I don't want to set this up on Linux (I use DropBox on Windows)

I also know there are third-party Linux launchers for GOG games, but I don't know if any of them can connect to the GOG API for playtime tracking and cloud saves

You know you must run the game from inside and in Galaxy for that to work. Did you manage to install Galaxy in Wine (or Proton or whatever)?

Hypothetically, yes. It'd probably be even more efficient than Windows; using proper versioning control in case a file got corrupted.
(This happens too frequently, it seems.)

In practical implimentation as is, Galaxy literally doesn't exist for Linux, as far as they are concerned.