You mean condenser instead of evaporator, the evaporator is inside the furnace and has no controls as it’s just a coil. The outdoor a/c unit contains the condenser and compressor and has the contactor (and controller if it’s an EC motor) for the compressor motor. The contactor control coil is 24v and the contact is closed when a call for cold is received from the thermostat.

Newer A/C units have EC motors with variable speed motor controllers and newer furnaces will have an EC motor blower fan and lots of factory control points wired up to a controller, mostly for the burner (and related gas/burner safeties).

Still, even in newer furnaces and a/c units, the thermostat is the main controller as like you said, the calls for heat/cool are the only input to the system.

Commercial HVAC controls for air handlers, boilers, and chillers have a lot more control points, an AHU can have 40 or more control inputs and outputs tied to it. Discharge and return air temp, multiple differential pressure sensors, static pressure, outdoor air temp, outdoor air pressure, duct avg temp, etc. These systems are much more complex than any home HVAC setup and usually have multiple controllers networked back to a master controller which orchestrates everything.