Am I right to understand the issue here is more about wheels keep turning after keyboard input started and player opens map? So would making wheels start turning towards center be enough? Mouse/analog steering doesn't have this problem in my tests, wheels stay where you left them, only keyboard turning seems to continue to extreme.

Yes, if there is active turning input when the player opens map, changes position, or exits vehicle, the wheels will continue turning in that direction. Repro Method 1 and 3 are the most noticeable in normal gameplay, as it is very easy to make some subtle mouse steering input when opening the map or leaving the vehicle. Results in a crash if driving with the map open, and getting back into a vehicle will notice the steering is at full lock left/right.

For the mouse input, the mouse must be moving at the moment the map opens (having turned wheels isn't enough). It doesn't matter if the input is towards the steering limit or towards the centre. The most obvious way to see the issue:

1. with keyboard, drive forward and turn right to full lock.
2. Release turn right key. Keep pressing forward.
3. move mouse slightly left. while mouse is moving, press M to open map. Keep pressing forward.
4. Observe the player's vehicle change to left turn full lock.

I've tested with XBOX controller and there's no problem.

Desired behaviour would be steering self centres when the map opens (same as tracked vehicles and boats). When player moves to another seat or exits vehicle, steering should remain at the current position, or if not possible, self-centring steering is preferable over current behaviour.

For the mouse input, the mouse must be moving at the moment the map opens

This is what I was missing

T153528 ticket might be worth merging with this

rev 148701 opening map, changing seat or abandoning car should result in steering autocentering @ceeeb please check

Confirm issue is resolved in Dev Build 2.09.148730.
Cheers KK