Maxwell writes:

It's honestly just one of those things that do not hold true to form on PC
simulators.

Real autopilots on real aircraft do not necessarily have control over the real
rudders, and yet they execute real coordinated turns without those rudders.
How do they do it?

But turns do not always have to be perfectly coordinated.

Why are they more coordinated when performed by the autopilot than when
performed by the pilot (without rudder)?

Especially shallow ones initiated by wing levelers or low end autopilots.

Autopilots often put the aircraft into a standard-rate turn, which isn't
exactly shallow, even if it isn't terribly steep.