A fully charged standard battery is 12.7 volts and typically a few 10ths less under load. When the trailer is plugged in and the converter is operating, the 12 volt
circuits will generally see between 13.2 and 14.4 volts depending on the converter's charge mode. So one would expect to see slightly brighter bulbs when plugged in. Perception of brightness can be subjective, so to better understand what is really going on, an inexpensive digital volt meter could be useful to determine if the voltage is really where it should be.
You could measure the 12 volts either at fuses, at one of the 12 volt
outlets, or directly off the battery posts.