There are a few values you can look at that are tracked in device configuration metadata that you could use to know when a device last was online:
- Last Configuration Send time - sent anytime your device connects / configuration is posted
- Last Event Time - Last time an event was sent from the device
- Last State Time - Last time state was sent from the device
- Last Heartbeat time - Last time MQTT heartbeat was sent
To get you started, here is an example using API explorer that you can fill-in with your project ID, region, registry, and device to query for a specific device's metadata.
For 1...3 you have control over these through device manager and by publishing data. MQTT heartbeat is updated if your device sends an MQTT_PINGREQ message during the "ping period" without other messages getting sent.
At any rate, you could use any of these update time values to see the last time a device was online / functioning. You could query the states of your devices after listing the devices in a registry and could update a Firebase RTDB periodically if that's how you want to report (e.g. using AppEngine TaskQueue). Note that you also just can get these "last connected" values from the Google Cloud Console.
It was said before but we don't have an event for disconnect, just configuration ack, which generally is the connection event. If you want to share state between a device and the device manager, use state messages.