No. A lot of the stuff GamePass uses on Windows, like UWP, haven’t been reverse engineered yet. And it doesn’t seem like there’s much interest to do so, outside of the occasional GamePass subscriber that wants to use Linux like yourself. Cloud Streaming with GamePass Ultimate is your only real option currently. And at best you can maybe hope that Microsoft will partner with Steam in the future to integrate it there in some way, similar to EA Play.
Valve employees have confirmed that the OLED display is incompatible with the LCD Deck’s Mobo. So you can’t upgrade just the screen.