Three thermostats, one HVAC system

Configuration
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2

Create another Template Sensor that applies the rules you defined.

  - name: PT HVAC Activity
    state: "{{ state_attr('climate.tstat_pt_thermostat', 'hvac_action') }}"
  - name: PP HVAC Activity
    state: "{{ state_attr('climate.tstat_pp_thermostat', 'hvac_action') }}"
  - name: Flex Room HVAC Activity
    state: "{{ state_attr('climate.tstat_flex_thermostat', 'hvac_action') }}"
  - name: HVAC Activity
    state: >
      {% set hvac = [ states('sensor.pt_hvac_activity'), states('sensor.pp_hvac_activity'), states('sensor.flex_room_hvac_activity') ] %}
      {% if hvac | select('eq', 'heating') | list | count > 0 %}
        heating
      {% elif hvac | select('eq', 'cooling') | list | count > 0 %}
        cooling
      {% elif hvac | select('eq', 'idle') | list | count == 3 %}
        idle
      {% else %}
        off
      {% endif %}

I added a final else as a catchall in case the state of the thermostats, for some unforeseen reason, doesn’t match any of the three tests.