Just found the remote play topic now, already created another one, but anyway, I'll just post it here again in case it wasn't already known:
The new Call of Duty: Vanguard beta can also no longer be played using the Remote Play trick. If you play the game via Remote Play, you can use all the buttons in the menus - but as soon as you start a game on a map normally, you can no longer use certain buttons:
So far I've noticed it with L1, R1, L2, R2, L3 and R3.
Unfortunately, with Remote Play, it is also no longer possible to play the latest version of Call of Duty in the PS5 version.