Large inverters have their own transfer switch.
No inverter power does not go through the transfer switch.
Incoming power from genset and shore power goes through transfer switch, then to a branch breaker that feeds the inverter.
You could have a partially tripped circuit breaker in the 120 power distribution panel.
Is your rig a 30 or 50 ampere shore power?
Start by resetting all citcuit breakers. Turn them all off applying light pressure toward off, then turn main breaker on, if equipped, then each branch breaker one a t a time.
