[mqtt.homeassistant] ensure availability topics get subscribed (#13466)

[mqtt.homeassistant] ensure availability topics get subscribed (#13466)

HASS registers availability topics before calling start(), so
the AbstractMQTTThingHandler was never subscribing/starting the
availability channel(s). So do so in start() of the base class.

I checked other implementations, and either they already handle
re-registering availabilityTopics in their start()
(GenericMQTTThingHandler), or they don't use availabilityTopics
at all from the base class and manage it themselves (Homie).

Note that this shows up as newly-added HASS things not having
a problem (because the components aren't discovered until after
the ThingHandler is started), but if you restart OpenHAB or
disable/enable the thing, the channels (and components) are
cached, thus how availabilityTopics are known before starting.

Signed-off-by: Cody Cutrer <cody@cutrer.us>