As we can see, all planes can only do 20 degrees turn during autopilot is on. However, not all the planes should only do this kind of shallow turn, for example. TBM-930 should be adjusted to 45 degrees, at least. All fighter aircraft should be at least 60 degrees, 70 is better. So I think that this function should be an option in the settings. I don’t think I need a photo to show so I just put down the description.
Autopilots are mostly set for 1 standard rate turn, meaning 360 degrees in 2 minutes. Some have an option for half rate turns.
The bank angle depends on your True Airspeed, not aircraft type and so on.
Quick formula to figure out the bank angle for one rate turn is
Bank angle = TAS/10 + 7