Have you ever managed to get it working? I am asking because we had a simmilar case with Tado yesterday. We used the service
climate.set_hvac_mode instead of
climate.turn_on. Your thermostat shows the same
hvac_modes: as mentioned in your post:
hvac_modes: - auto - heat - 'off'
You could also try this blueprint and tell us if it also works for you and your HM-CC-RT-DN Thermostats. Thanks in advance!