Cars don't steer right with controller

Yeah, in Options > Controls > "Find and click the bindings related to 'Steering" > Another window will appear on the right with many settings, including deadzones.
A dead zone should not prevent you from turning entirely in a direction. They only cause small movements to not be registered, or small movements to be registered when you did not move the thumbstick.
Try to reset your bindings (Options > Controls > Reset All)

 

Go to Options > Controls > Hardware and test your thumbstick there.
Is it working correctly? Is it reporting the same inputs you are giving it?

 

That menu shows the raw inputs the game received.
If it's not working there, it means it's either your controller, or some program that is intercepting your bindings and messing with them.

To try, see if it's Steam doing that.
Go to Steam > Settings > Controller > Controller Settings and make sure no box is checked.
Close, and check again in-game.

If it works fine now, it means Steam was intercepting and messing with your inputs.

 

Test your controller within Windows directly:
https://www.howtogeek.com/241421/how-to-calibrate-your-gaming-controller-in-windows-10/

Search for this line on that website:
"The window that follows will contain two options: Settings and Test.
From there, go to the Test tab, and from there you can test the controller (what Windows receive).

If the controller is acting up there too, then it's potentially the controller itself.

 

What do you mean?
The same issue occurs inside the Windows 'Controller Tester' tool?
If yes, then that means the problem is not coming from the game or your PC, but the controller itself.
Possibly the controller is defective, I'd suggest returning it back or get a replacement if it's still possible