I'm not sure on your inverter charging profiles, ie; what voltage is bulk phase (step 1) and what voltage is float phase (step 3). Judging from your earlier posts I suspect float is 13.6V which is good, and most inverters have 14.6V bulk voltage.
LFP battery has a very flat charge curve so 13.3V is in the middle of the flat curve and will sit there for a very long time while charging.
Because LFP voltage curve is different from LA, you need to ignore the inverter battery % on the front panel, only look at voltage.
Try draining the battery down to 12V, then charge it back up so the charger can go through the normal cycles. I suspect it is confused as a starting voltage of 13+ volts is a fully charged LA status, where an LFP battery can be anywhere from 30% SOC.
Here are the resting values, take note while charging these will be slightly higher:
View attachment 1433321
You don't mention how many amps your charger is?