I did not see an actual converter there. The panels in the first photo look like separate AC/ and DC panels which suggests the converter is... Somewhere else
I agree with Drew, 13.5 Volt loois like a single stage converter typically 13.6 but I'll chalk that last 1/10 volt to meter error)
Too many possible things to list so I'll do the other list.
When you check battery levels.. EVERY THING OFF save the indicator panel.. No shore power, no lights, no fans, turn off the fridge, everything off for a true reading, and even then I'm not sure how accurate the panel is.
Loads will lower the reading
Shore power SHOULD increase it.