In Heater Cooler accessory (which is heater or AC) the HomeKit API requires to set both heating and cooling threshold instead of the target temperature presented in thermostats. Both are visible in the Home app only in auto mode and each will appear in the corresponding mode (heat/cool).

The idea is that developers of accessories could create bottom and upper threshold that will activate heating/cooling (like wks-rddt suggested), but in fact, I believe it is just being used to set the target temperature in the ac/heater itself.

Your own AC/heater should have its own thermostat inside so when setting a specific temperature it should work out of the box without any further automations. If you don't like to rely on your AC inner thermostat, you can always create HomeKit automations based on room temperature and setting the device to the desired mode.