Since #36479 mqtt sensors are set to 'unavailable' on HA restart

[VDRainer]

The problem

CC @definitio
In beta 0.112 on HA restart, mqtt sensor states go to unavailable.
Looks like since #36479 the mqtt connection is disconnected before HA shutdown is complete and so mqtt sensor states are stored 'unavailable'.

Environment

• Home Assistant Core release with the issue: 0.112.0b2
• Last working Home Assistant Core release (if known): 0.111.4
• Operating environment (OS/Container/Supervised/Core): Ubuntu 18.04, Python 3.8.3 venv
• Integration causing this issue: mqtt sensor
• Link to integration documentation on our website: https://www.home-assistant.io/integrations/sensor.mqtt/

Problem-relevant configuration.yaml

The following automation sends a notification
"There are unavailable ubuntu updates available."
on HA restart before HA shutdown is complete

sensor:
  - platform: mqtt
    name: tpad_os_updates
    state_topic: 'home/sensors/TPAD/os_updates'

automation:
  - alias: Update notification OS TPAD
    initial_state: true
    trigger:
      - platform: state
        entity_id: sensor.tpad_os_updates
    condition:
      - condition: template
        value_template: "{{ states('sensor.tpad_os_updates') != '0/0' }}"
    action:
      - service: notify.mobile_app_rainer
        data_template: 
          title: "TPAD OS Updates"
          message: "There are {{ states.sensor.tpad_os_updates.state }} ubuntu updates available."

Temporary fix:

      - condition: template
        value_template: "{{ states('sensor.tpad_os_updates') != '0/0' and states('sensor.tpad_os_updates') != 'unavailable' }}"

Traceback/Error logs

Additional information

https://discord.com/channels/330944238910963714/427516175237382144/726724658258247711

[definitio]

I'll look into it.

[balloob]

Can be easily fixed by checking inside async_mqtt_connect if hass.is_running before writing the state.