A321 Captain reported APU failure during push back.

Narrative

During pushback and prior to engine start; the APU failed and the aircraft went dark except for the items on the DC/Battery Bus. I was still able to communicate with the tug driver and still had access to comm 1. The FO lost everything on his side. I asked the tug driver to remain on headset until I could figure out if we could get the APU back online. I was just about to restart the APU when the Tug driver said his wing walker saw smoke coming from the APU. I elected to not restart the APU and asked the Tug to bring us back to the gate. As we were being towed into the gate; we lost all electrical power and the batteries dropped below a useable voltage. This was pretty concerning because smoke had just been reported and now we didn't have any way to communicate with the ground crew; the flight attendants; or ATC to possibly request emergency equipment. It also meant we lost fire detection and fire suppression abilities. In addition; the PA system was not usable. Luckily we had already coordinated a return to gate so the tug brought us in and a jet bridge driver was waiting for us. I felt a lot better once we had the door open and ground power was hooked up to restore the aircraft to a mostly normal configuration. The time between loss of AC power to battery depletion was less than 5 minutes. In addition to loss of any kind of fire detection with passengers onboard; I was also unable to set the parking brake once we got back to the gate. I was able to use hand signals to ask for chocks. After arriving back at the gate; the aircraft was taken out of service. We swapped aircraft and continued without further incident.For what it's worth; both the APU and batteries were written up in the several days prior for the same issue. I'm glad this happened while we were still attached to the Tug or this could've gotten really ugly if we had no comms to call and get towed back to the gate. Overall; thanks to the ops center for coordinating the return to gate and calling an agent over to drive the jetbridge so quick. And thanks to the Tug driver who really helped us out despite losing comms with him on the return.