Thermostats in Homekit integration

Hi,
I am a fresh Home Assistant user and so far, all is going well.

I have set up a few devices including Devolo radiator thermostats.
They show up fine in the frontend and I can control everything as expected.
However, I am trying to use the homekit integration and for some reason, the thermostats don’t show up.
ocnfiguration yaml looks like this

homekit:
  filter:
    include_domains:
      - sensor
      - climate
      - switch
      - light
    include_entities:
      - climate.danfoss_devolo_home_control_radiator_thermostat_heating_1
      - sensor.danfoss_devolo_home_control_radiator_thermostat_temperature
      - sensor.danfoss_devolo_home_control_radiator_thermostat_battery_level

all lights and switches show up fine in homekit but the thermostat does not…

I double-checked for typos, checked the yaml file format and everything.

Do I have to specify anything for the entitiy to make homekit recognize it? Does anyone have an example? at first I thought, simply adding the “climate” domain was enough, but no. Then I added the specific entities but still no luck…

thank you for any advice