https://www.zoom-platform.com/news/all-flatout-games-have-been-updated-with-mod-support-and-more-on-zoom-platform-and-steam
The FlatOut trilogy is now Steam Deck verified, with Workshop support, new languages, improved graphics, and revived FlatOut 2 multiplayer.
Bought Flatout 1 and it runs really great! I also kind of like that the game is pretty bare bones, it doesn’t has 1000 mechanics and it’s really great for casual play.
If you are looking for spiritual successors to the Flatout formula, Wreckfest is the first place to go.
https://isthereanydeal.com/game/wreckfest/info/
Obviously it doesn't have all the same vibes and minigames, but it totally embraces a similarly chaotic style of racing vehicles like you actively have a vendetta against them and want to destroy them in the process of winning the race.
If you want a physics sandbox that runs great on the Steam Deck, don't sleep on Rigs Of Rods, it really doesn't get enough love and the project is REALLY mature at this point with a ton of vehicles of a wide variety that are near professionally made and rival what paid games have to offer easily.
(it is worth nothing that Rigs Of Rods has an ingame mod repository browser so you can easily download community content which is awesome).
If you want realistic physics and a sandbox experience check out the superb Motor Town. Not strictly a racing game but especially when you factor in tire grip and burnout physics simulation Motor Town has some of the best feeling vehicles period in any driving game.
https://store.steampowered.com/app/1369670/Motor_Town_Behind_The_Wheel/
If you want something goofier and even more arcadey check out Wobbly Life which is like GTA for kids but also a game made for adults that is superficially about being a game for kids (how old is the kid the player takes control of who is kicked out by his grandma to earn money reallllyyy? Mental but not physical maturity is clear). The thing is, the driving feels good, it feels challenging. It is silly, janky and fundamentally absurd but also it is a fun chaotic driving game so I think it deserves to be recommended along with these other Flatout alternatives.. I also think the underlying vehicle physics are good enough that someone could easily implement a realistic vehicles mod.
https://store.steampowered.com/app/1211020/Wobbly_Life/
This recommendation is partially in a different genre, but Offroad Mania is a superb steamdeck driving game with very realistic physics and sandbox levels. The best modes it has are mini technical offroading challenges and an endless rock crawling course that is randomly generated until you fall off (you try to get as far as possible).
https://store.steampowered.com/app/1222040/Offroad_Mania/
All of these games run great on the Steam Deck