The animation shows the inner "cylinder" being resized as the tank is filled/drained with water. Assuming that's a realistic representation, that implies the air is basically in a balloon inside the tank. Outer shell will have to handle the pressure of the most compressed state (ie, at a full 300 bar fill + however much volume of water you need to add to become neutral in order to decsend). This also implies the pump needs to handle pressures in excess of 300 bars.
Concerns about loss of battery/pump I don't see so much as a problem. As long as you still have air left the "dump valve" simply uses the pressure of the gas to push the water back out, and voila, buyoancy. And it appears that the aim is to be neutral anyway, so should always be able to swim up at which point wetsuit decompression etc will start making you marginally positive.