I too thought inverter was running everything with low batteries but the OP said it was not on.
As suggested, what is the voltage at the pedestal when you run the microwave. If it drops then the problem is not the RV. I would check all electrical connections on the 50 amp circuit. A loose screw can cause these issues. Check the circuit breaker on the house/pedestal. Turn it off then put in a large flat blade screwdriver and turn the screw on the CB, if its loose snug it down. Also check connections on the transfer switch as well as the circuit panel in the RV. If any of the connections are loose it can create this issue. Make sure power is off and you have a insulated screwdriver so you don't electrocute yourself.