I believe stabilization is an option with some of the more recent autopilot kits that can be purchased with the aircraft or as an upgrade, but the aircraft represented in the sim seems somewhat old school (I’m not even sure they make the non-G1000 instrument panel anymore for new airframes coming off the factory line) and likely doesn’t have that modeled.
If I understand correctly, I think the ones so-equipped have a panel in the lower stack that looks like this, and one of the modes or a combination thereof enables stabilization:
