Well this is BS because:
1 - In almost all instances, Proton runs Windows games with equal or worse performance on Steam OS (translation layers require CPU cycles) and fewer features available (like raytracing). It's not like the translation layer isn't coming at a cost because it is, and Microsoft isn't making GamePass available to SteamOS which doesn't exactly bring them any favors to their point, to be honest.
2 - Steam Deck has no Call of Duty?
Save for the latest one, all the others that say "unsupported" work just fine. I actually finished CoD WW2's single player campaign last week on my Steam Deck and it played great. Almost all CoDs claimed as "unsupported" are running a splash page unsupported on Linux, which is easily circumvented with a command line in the game's settings.
If they're trying to convince regulators with these claims, they shouldn't make such blatantly false statements that are easily countered with a quick search.