What's even more amazing is that back then I had the luck to find this thread and this other thread which also had the same problem. Because the most I got out of checking logs and debugging coredumps, was this ReadCursorFromTheme error (repeated like 10000 times).
Also, I had the default cursor pack and like with OP, it just stopped working one day. I'm guessing it has something to do with how hyprland tells the apps what cursor to use (hence the hyprcursor thing OP mentions), but honestly I don't even want to think about it anymore, it made me lose a whole day back then xP
It does support Linux: it lets you download Linux installer for games that have a Linux port.
The lack of GOG Galaxy on Linux just means you have to manually manage your games.