Third option is to ensure the downloader runs under proton, which I think it does but haven’t tried.
https://gogapidocs.readthedocs.io/en/latest/
The problem is mostly that their backend isn't wired for Linux builds so you can't use the APIs for native Linux versions.
However, neither support 2 key features of GOG Galaxy:
1. cloud saves
2. achievements
These are 2 of the most significant features of competitors like Steam, IMO, so missing them for GOG on Linux is unfortunate.
Please don't lie :/
If you think that's a "lie", consult a dictionary.
As for whether my general point stands, I think it's a reasonable inference that if GOG Galaxy supported Linux, it would support Linux games and cloud saves for those games, and only then would Heroic and the like be able to implement such a feature. I could be wrong, as it depends on details I don't know, and I'm just making an educated guess.
Given I'm using Heroic from AUR on a supported OS, and installed with default settings, I consider this cloud save support to be less than stellar, but that's a separate matter, I'm not trying to turn this thread into a support issue.
As for achievements, I wouldn't say it's had support for "a long time"; they were added in August 2024 (v2.15.1).
The whole point of GOG is that you don't need a "client" -- it's just a store.
If you want to use something other than a standard web browser to install your games, there are plenty of options, including projects like Lutris and lgogdownloader.
Their Galaxy backend only handles Windows and macOS builds of games. Linux builds aren't included now. There are hacks around it like using access to individual files over HTTP through zip format for Linux installers as pseudo Galaxy (lgogdownloader supports that) but it's still just a hack.
Another piece is multiplayer integration that games can ship. That depends on their support too (authentication, matching and etc).
But again, the whole point of GOG is that you don't need a special client in the first place. You just get ordinary installers, and don't have to deal with the game requiring a third party's proprietary launcher.