core: EQ3 Thermostat - Unable to control via Google Assistant integration

Home Assistant release with the issue: 0.79.3

Last working Home Assistant release (if known): not checked with any older versions

Operating environment (Hass.io/Docker/Windows/etc.): Virtualenv on RPi

Component/platform: Climate/EQ3 Bluetooth Smart Thermostats

Description of problem: Thermostat works properly from the HA, I can control it, everything works fine. Thermostat is displayed in Google Assistant and is assigned to the room as other my devices.

When I try to set temperature via Google assistant: me: set small room temperature to 21 ga: That mode isn’t available for the Grzejnik w pokoiku

“Grzejnik w pokoiku” is a customized name

and addidtional GA reply with current thermostate temperature:

As @awarecan wrote in this issue (hiden comments): #17302 ,eq3btsmart.py do not support STATE_COOL, STATE_HEAT: https://github.com/home-assistant/home-assistant/blob/3f87d413813de84935ea67b5212c55348524447f/homeassistant/components/climate/eq3btsmart.py#L64-L71 which are supported and required by google assistant: https://github.com/home-assistant/home-assistant/blob/3f87d413813de84935ea67b5212c55348524447f/homeassistant/components/google_assistant/trait.py#L408-L415

a similar problem has been positively solved for climate/Zwave https://github.com/home-assistant/home-assistant/issues/13158

Is it possible to introduce similar changes also for EQ3 Thermostat component?

Problem-relevant configuration.yaml entries and (fill out even if it seems unimportant):

climate:
  platform: eq3btsmart
  devices:
    small_room:
      mac: '00:11:22:33:44:55'

customize:
  climate.small_room:
    friendly_name: Grzejnik w pokoiku

cloud:
  google_actions:
    filter:
      include_domains:
        - switch
        - light
        - group
        - vacuum
        - climate

google_assistant:
  project_id: someprojectid
  client_id: someclientid
  access_token: sometoken
  agent_user_id: someemail
  api_key: somekey
  exposed_domains:
    - switch
    - light
    - group
    - vacuum
    - climate

Traceback (if applicable):

Additional information: