I have no idea what is causing this, and the CyberPower website doesn't even list this particular issue in their list of "all beep codes".
All I did was take out the old batteries and replace them. Pretty simple and straightforward, except this keeps happening and I don't know why.
I have disconnected the battery, held power down for 30 seconds, and reconnected it, but no change.
Video demonstration of issue:
111 Answer
As it turned out, according to Cyberpower this sounded like a POST failure, but since the UPS was plugged into mains power, it just kept trying forever.
So I took everything out one more time, and it looked like the terminals on one battery had wiggled loose. I reconnected them again being very very careful they stayed connected this time, put it all back together, and voila - all is good!