By setting birth and last will messages, upon restart Home Assistant advertises it’s presence to the MQTT broker. This in turn triggers the MQTT hub app of Homey to broadcast all the devices and their state to the broker which Home Assistant uses to repopulate the devices… When set successfully, there should be no need to reboot the Homey hub or client app after a Home Assistant reboot, just wait and the devices will turn from unavailable to proper state. You can actually observe this while opening the settings of the MQTT hub app on Homey and restarting Home Assistant: you will see the green bar of broadcast start automatically!