I think you have to enable the availability check at the settings of your zigbee2mqtt webpage. To do that, go to the webpage of your zigbee2mqtt instance, go to settings, availability and activate simple or advanced.
Yes, with a small wildcard it’s possible. Everytime a device changes its availability you get the payload “offline” or “online” on topic “zigbee2mqtt/+/availability”. The wildcard (+) will later be replaced by z2m with the real friendly name of the device.