I tend to do my Steam shopping in the browser and I use the ProtonDB-Peek userscript. This gives a ProtonDB status badge in the right column under the review links.
Apparently, this is a browser extension (well, a script for a browser extension), so it works when you browse the Steam catalog through your web browser, but not through their client. Or did I miss anything?
Correct, that's what I meant to imply in the first part of my comment. When I research new games I do that from a web browser and that's when I care about Proton status the most so this works great for that. It does not help when using the Steam client.
Yeah, when I made the switch, I checked a bunch of the games I played the most for steam deck compatibility and thought I had to give up on some of them, only to find that they were still fine because my desktop is much more powerful than the steam deck. Plus it has a keyboard; if a game requires a keyboard, it hurts the steam deck compatability score (how much depends on if it's required for playing the game at all or just needed every now and then to enter some text).
So treat "steam deck supported" as "works on linux" and "steam deck unsupported" as "maybe works on linux".
I think the better indicator of not supported at all on Linux is the "3rd party kernel anticheat" marker in the store, though I tend to avoid games with that anyways, so I can't really say for sure.