If you're talking about playing natively games on the Game Pass, you can't as of right now there's no Xbox app to download and launch them on Linux.
Otherwise, if you meant streaming games from the cloud through Game Pass, then the answer is "it depends from your connection", but i am quite satisfied with the experience so far.
I'm on a 1Gpbs optical fiber, games run well, i get some-to-zero graphic artifacts and even though you can feel some baseline lag, for most games it's fine and you'll get used to it in a minute or two.
Is there no way to get game pass running on the deck? I installed some emulators, and a friend of mine installed Diablo 4. I just assumed someone figured out how to get game pass working.
Not as far as i know, the Xbox app to start games through Game pass is available only on the Microsoft Store and there's no way to get that up and running using Lutris or another kind of virtualization layer
it IS possible to play Game Pass games on the deck, but you would need to install Windows 10/11 on it to do so. You could either wipe out SteamOS completely, or dual boot SteamOS and Windows and have the best of both worlds. Windows advantage is you are able to play any game, including those that have anti-cheat that block SteamOS. However it can be a little bit clunkier to navigate since it's not designed with a controller-first interface
Your only chance is installing Windows on deck. Which is possible, but far from enjoyable IMHO.
My limited understanding is that Gamepass games are distributed in some Windows only package/format („stuff that you download from the windows store“) that does not run on Linux/SteamOS, emulated or natively.