Unfortunately a lot of the new variable-speed heat pumps require a proprietary thermostat. You can use a dumb thermostat with them, but then the unit runs at full tilt all the time, which is inefficient (more costly to run) and probably increases wear on it.

Fortunately there are some heat pumps that allow you to use any old thermostat; they figure out the right speed to run at using their own temperature sensors.

Regardless, this wasn't really the thermostat: this was a control system that monitors temperatures in each room/zone, and opens and closes the vents to hit the temperature targets in each zone. Pretty sure no dumb (or even generic smart) thermostat can handle that.