How to trigger on any action of an Zigbee2MQTT device?

What you want is possible if you use a State Trigger to monitor the device’s Event entity.

It will look something like this:

alias: Example
triggers:
  - trigger: state
    entity_id: event.your_device_action
    not_from: unavailable
    not_to: unavailable
conditions: []
actions:
  - variables:
      btn_evnt: "{{ trigger.to_state.attributes.event_type }}"
  - choose:
      - conditions: "{{ btn_evnt == 'on' }}"
        sequence:
        ... actions to perform when button event is `on` ...
      - conditions: "{{ btn_evnt == 'off' }}"
        sequence:
        ... actions to perform when button event is `off` ...
      - conditions:  "{{ btn_evnt == 'left' }}"
        sequence:
        ... actions to perform when button event is `left` ...

An alternative is to use an MQTT Trigger to monitor the device’s MQTT topic.