There are plenty of games that are very specifically targeting Proton compatibility at a very minimum thanks to the Steam Deck, so I'm perfectly happy with any game that's developed with that in mind.
Being verified on Steam Desk is my parameter for deciding if I'll consider a game or not, even if I don't have a Steam Deck (yet). I'm perfectly fine with that, not asking for a Linux native version as long as the game works as it should on Proton.
Verified is probably a stricter metric than you need/want. Many games aren't verified just because of font-size issues and the like on the small screen.
I'm on Linux Mint right now and when I go my library and toggle the "Show only games that run on Linux" button, nothing happens. I don't think Valve cares about the distinction, so long as it runs.
if you have proton enabled the library shows all games as linux compatible. If you disable proton in the steam settings on linux the filter will only show games that run natively