Forza Motorsport just launched and sadly it appears that it does not currently run on Steam Deck / Linux with Proton, but Valve are looking into it.
This entry in the series comes from Turn 10 with Xbox Game Studios publishing and it seems something about the tech behind it is causing problems with Valve's Proton compatibility layer. In reply to a user on social network X mentioning it not working, Valve developer Pierre-Loup Griffais mentioned "It doesn't work in Proton, we are looking into it."
Sadly, it seems Forza Horizon 5 was also updated, and this has also now been broken so we're seeing a bit of a double whammy on compatibility issues with these racing games now.
While Valve may be able to find the cause of the issues in Proton, it may also require the game developer to do some tweaks on their end, so hopefully Valve will be able to speak to Turn 10 / Xbox Game Studios on the issues. In the past we've seen Xbox Game Studios talk-up their titles running on Steam Deck so it would be a shame to see these left broken.