You can't run yuzu or Cemu on PS even if you wanted too. The Sony's platform is tremendously locked. Also I mentioned Proton in my original post, you get Linux compability for the "Microsoft exclusive" game basically for free.
I can't run Halo Infinite or Forza Horizon 5 on PS5 either regardless if I wanted to.
You got my hopes up:/ I just looked and I don't see a single COD game showing proton/steamdeck support on steam. Maybe there's workarounds for some of the old ones, but I don't think any recent ones with working anti cheat have anything but Windows support.