Yeah this is an odd issue at this current time with Steam Controller Config. You used to be able to select generic controller config and the Xbox 360 controller would work. Not sure if Xbox 360 controllers work anymore. I do believe I had it running well with Xbox One controllers but it no longer works. It really bothers me as this game is a top game and the Steam Controller configuration shouldn't bug around with games natural settings.

https://github.com/emoose/OutRun2006Tweaks
Use this mod.

I initially had issues even with the mod using my Series S controller. It's Steam interfering with it and overriding the built in controller support. When the game loads, open the Steam interface and disable Steam controller support. It will then default back to the games's built in controller support and work normally.