It is the same on Xbox and Logitech G923 and at the beginning I didn't understand why the wheel seemed to disconnect itself. To avoid this I have to launch the game and confirm the loading screen (see screenshot), with the wheel and the game should identify the wheel as the primary controller.
If there is a doubt, you can check in the options, in controls, the primary controller is indicated (see screenshot).
For your other issue, there is an option in the vibration menu of the wheel, "steering centre force" that should realign the wheel in respawn or restart.
I hope it helps.