MQTT: Publish "stopped" to available topic on app stop (#22527)

* Publish "stopped" to available topic on app stop

* Add docs

docs/docs/integrations/mqtt.md

@@ -11,7 +11,8 @@ These are the MQTT messages generated by Frigate. The default topic_prefix is `f
 
 Designed to be used as an availability topic with Home Assistant. Possible message are:
 "online": published when Frigate is running (on startup)
-"offline": published after Frigate has stopped
+"stopped": published when Frigate is stopped normally
+"offline": published automatically by the MQTT broker if Frigate disconnects unexpectedly (via MQTT Will Message)
 
 ### `frigate/restart`
 

frigate/comms/mqtt.py

@@ -38,6 +38,7 @@ class MqttClient(Communicator):
         )
 
     def stop(self) -> None:
+        self.publish("available", "stopped", retain=True)
         self.client.disconnect()
 
     def _set_initial_topics(self) -> None: