If you want to stream from your gaming PC, just start Steam on the gaming PC, login to the same account, and then your Steam Deck's "PLAY" buttons in the library should have drop-downs that let you select "STREAM" instead. It should work whether the host PC is running Windows or Linux or Mac, but of course you'll have a bigger library selection if the host is on Windows. (To be clear, the host PC can run any Windows game and stream it to Steam Deck running its default OS; no need to add Windows to the Steam Deck).
Ahhh I see what you're asking now. Sorry, I misunderstood.
Yeah, I think you'd have to run Windows :( Even if the games were supported via Proton, I think (but I'm not sure) that Gamepass adds its own DRM layer.
If you do have a separate Windows machine though, streaming actually works very well... better than the Deck on its own... better graphics, way less heat/fan/battery life consumption (since the computer is doing all the hard work). I'd try if you haven't already.
If you want to stream from your gaming PC, just start Steam on the gaming PC, login to the same account, and then your Steam Deck's "PLAY" buttons in the library should have drop-downs that let you select "STREAM" instead. It should work whether the host PC is running Windows or Linux or Mac, but of course you'll have a bigger library selection if the host is on Windows. (To be clear, the host PC can run any Windows game and stream it to Steam Deck running its default OS; no need to add Windows to the Steam Deck).