However, let’s face it, Valve isn’t about to just let Microsoft run a GamePass app on SteamOS either.
SteamOS is Linux (Arch). If Microsoft wanted to put GamePass on Linux, there's no reason it wouldn't run on a SteamDeck. Valve isn't trying to create the same sort of "walled garden" which you get with other consoles. I have several games loaded up on my SteamDeck which aren't from Steam. And I can even add them to the Steam interface. Microsoft software not running on the SteamDeck is entirely Microsoft's choice.