I think their original intent back when Proton originally launched was to just show generic Linux compatibility on any titles if it worked with Proton and was approved by Valve. I’m not sure why they stopped doing that.
Probably they understood that they couldn’t realistically check every new and old game out there and that people could patch games themselves, so it would be kind of misleading and pointless. Just like SteamDeck now: you get the “not-compatible” warning with working games that don’t have a nice starting UX but that works just fine
They could add an optional plugin that uses protondb to get a quick overview of compatability
ProtonDB isn’t a Steam product though, it’s a crowdsourced community effort built and maintained by users. Steam pulling that into their official infrastructure would immediately put a ton of technical stress on the project. It would also be pushing on that boundary between a corporation supporting a community project and drafting all its volunteers as unpaid labor.