13.6 isn’t usual depending what phase the charger is in. Depending on the model and features the charger has it will sometimes send as much as 14v to the battery for a short time near the end of a charge cycle and then drop back down to around 12.8 to “float” charge the battery. You need to check it periodically through the day and see if maybe it’s stuck in a boost mode or something and never dropping the voltage back down.
Don’t take the fact that your dealer said your charger is fine. They are far from experts at most anything to do with campers unfortunately. This forum is full of dealer and technician stories that make you hair stand up.
1999 Suburban 2500 4x4
2016 Jayflight 23RB Elite, Fiberglass, Polar Package
400w Renogy RV solar kit w/ Bluetooth, 100w Renogy solar suitcase
430 amp/hr 6v battery bank
1000w Renogy hard wired inverter
2011 F350 Lariat, DWR 4x4, 6.7 turbo diesel
2017 Open Range, Mesa Ridge 374BHS