If you actually use two 120V circuits that way and one breaker flips the other half will send 120V through the load back into the other circuit. So while that circuit's breaker is flipped it is still live. Very bad. Much better to use a 240V breaker that picks up two rails in the panel.
I assume the device has two separate PSUs, each of which accepts 120-240V, and neither of which will backfeed its supply.
i am guessing, without any proof, that, when one breaker fails the server lose it all, or loose two GPUs, depending on whether one connected to the cpu side failed.
They make connected circuit breakers for this use case, where one tripping automatically trips both.