I just had the house batteries replaced with AGM's. I checked the built in "battery control" and voltage was reading 8.85. This was one week after install. I started the generator to exercise it, the ...
At 13.3 volts I would stay plugged in with the battery switch on.
Down to 8.85 may have already damaged the batteries some with loss of capacity.
Damage to batteries was from old trickle chargers set at 13.8 volts combined with poor maintenance of the water levels. Does not apply in your situation.