I think the solution to the problem is here:
I think you are using the new (without telling you they changed it) rudder controls.
The new controls don’t re-center the rudder after you touch it. Follow this and let me know if it fixes it.Search for rudder by name under the gamepad.
See rudder left (yaw left) and rudder right (yaw right)?
Click on each one and clear current input and validate.
Click on rudder axis left or right and make the input left trigger for left and then right trigger for right and validate after each one.
Asobo needs to add it to the release notes and the Q&A in the stickied post above.