Way back in June 2018 I asked a question about my Eaton 5P 650 UPS and the 0x607 battery fault error it was reporting.
It took eighteen months, and it's far too late to update the previous thread, but I finally had a chance to track down the fault properly.
The problem was a failing capacitor - marked on the board as C39. I replaced the cap, put in fresh batteries, updated the firmware, and now the unit is working 100% as good as new again.
I have no idea whether this is a common fault or not, but I wanted to post an update here in case anyone has the same fault and Google sends them here.