Just note that (unless they've changed the default), you need to enable a setting in Steam to make it always use proton, or it will look like reality matches up with your previous expectations. I believe the setting is under compatability in the steam global settings.

Also be aware that the steam deck compatability icon cares about two things that might not apply to a linux desktop: it loses points for keyboard/mouse centric games (which work fine if you actually use a kb/m instead of controller), and it also cares about how that game will perform on steam deck hardware, though if your gaming PC isn't very strong, that one might be useful for you.

Protondb has the more accurate compatability info, though it's crowd sourced, so might not have up to date info on more obscure titles (though it does seem kinda like every single game has at least a small community obsessed with it that consider it the greatest game).