Coordinated turns without rudder, and autopilots

Paul kgyy writes:

As others have posted, most lightplane autopilots don't adjust the
rudder for adverse yaw when turning, so you do get a few seconds of
slightly uncoordinated flight. However at normal cruise speeds this
creates no hazard or discomfort.

So in theory I should be able to turn myself with ailerons only in the same
way, without the need to use the rudder to stay coordinated. What's the
secret? Each time I try to turn at the same rate that the AP manages, I have
to use the rudder to stay coordinated.

If flying close to stall, the autopilot should be turned off even for
straight and level flight. If the airplane is on the verge of
stalling and starts to turn because of engine p-factor or any other
reason, the autopilot will attempt to correct with aileron. This may
actually induce stall on one wing, producing sudden wing drop and a
potential spin.

I have an aversion to stalls and I usually stay well away from them. The AP
will put the aircraft into a stall if airspeed is too low to maintain altitude
easily (I don't know if this is an artifact of simulation or just like the
real thing--I know my simulated autopilot doesn't have all the modes of the
real one).