Presumably if there isn't a user report for whatever distro I'm using

Distro is unlikely to matter, as long as you don't pick a really obscure one. And even then, flatpaks will probably work fine.

Protondb also looks to be focused on Steam, I'm guessing it's like MacOS where if it's a game not on Steam then you're shit out of luck if there isn't a Linux specific version?

Steam is the easiest to work with and most well-supported. But there are other managers like Heroic Launcher and Lutris that can cover non-steam. Knowing whether a game can run on proton/wine outside of Steam does likely require a google search, though. Most things can be made to work as long as the game doesn't require kernel-level anticheat (e.g. Destiny and BF6).