First, I would disregard the push button battery indicator. Get a DVM (digital volt meter) from Harbor freight and actually measure the voltage at the battery or at the converter fuse panel on the DC side. The circuit breakers are for AC power.
As to the microwave operation, what you are likely seeing is a voltage shift on the ground connection. This can easily upset the accuracy of the button LED panel which is more of and indicator as opposed to displaying actual voltage or state of charge.
The AC ground connects to the frame.......somewhere, and the DC converter/battery negative will connect to the frame.......somewhere. Find those two points and make sure the connections are clean and tight. I found ours under the trailer AND...........the connection was made by a single #10 sell drilling screw which was loose and rusty. That got promptly repaired using proper size stainless steel hardware and by replacing with proper terminals on the wires.
Make sure battery connections are clean and tight. With shore power disconnected, check the screws on each of the circuit breakers in the converter. Don't forget to check the white wire connections on the neutral buss bar and also check the screws on the copper wires on the ground buss bar.
Bob