Motortown has by far the most realistic and fun driving mechanics of any game that will run on the deck besides beamng, and the fun thing about Motortown is all the different jobs like taxi, trucking, pizza delivery and many others. It has racetracks and a custom racemaker but it isn’t strictly a racing game though I almost exclusively play it as such (timed taxi rides). I basically play Motortown like Midnight Club: Please Help My Taxi Driver Has A Deathwish -edition

https://store.steampowered.com/app/1369670/Motor_Town_Behind_The_Wheel/

Offroad Mania is a rockcrawling quasi-racer. It has superb handling and softbody tire physics. Of note is the infinite obstacle course mode.

https://store.steampowered.com/app/1222040/Offroad_Mania/

Don’t sleep on the open source (with splitscreen) Stunt Rally 3, it is on the Discover app store in desktop mode. Don’t pass over the game just cus it at times has a silly theme, the tire grip mechanics are great and highspeed gravel driving feels great. In particular the rewind button is very nicely integrated too.

https://github.com/stuntrally/stuntrally3

There is also the venerable open source physics vehicle sandbox Rigs of Rods . Yeah it is old but it is still in development and the aged graphics = lots of battery life

https://www.rigsofrods.org/

If you want just a damn good rally game that does what it says on the tin and feels good mechanically check out Rush Rally 3.

https://store.steampowered.com/app/2020860/Rush_Rally_3

If you want more combat driving than racing checkout:

Endgame Road To Salvation

it has splitscreen, and it is awesome! The most apocalyptic caravan simulator you can imagine

https://store.steampowered.com/app/1264920/Endgame_Road_To_Salvation/

Chaos On Wheels

splitscreen, this one is a really good car combat game like twisted metal or vigilante 8. It isn’t really a racer I suppose.

https://store.steampowered.com/app/1623120/Chaos_on_Wheels/

Ashes Of The Union

roguelite monster fighting car combat game

https://store.steampowered.com/app/3091390/Ashes_of_the_Union/#app_reviews_hash

If you want to tool around (splitscreen) in arcadey cars in a family friendly humans fall flat crossed with gta game checkout Wobbly Life

https://store.steampowered.com/app/1211020/Wobbly_Life

The all time best racing game on the deck is most certainly Bunny Hill however (of course it is splitscreen!).

https://store.steampowered.com/app/1424350/Bunny_Hill/

One final odd suggestion, you can definitely fly drones in a drone simulator with onboard steam deck controls I don’t care what quadcopter people say. Liftoff is a blast, has a racing community and the freestyle maps are a joy to swoop around.

https://store.steampowered.com/app/410340/Liftoff_FPV_Drone_Racing