He plugged the oven directly into the bed receptacle. That should have worked. It didn’t. The truck has a problem.because you are having issues with 'electronics', not necessarily 'electrical' issues since the HVAC is running(compressor)... I would lean toward a Ground or Neutral issue, since electronics have a MUCH more requirement for stable connections. The a/c unit probably doesn't care much. Lights don't care, etc.
I wonder if the GROUND for the rear INVERTER is the issue, since the front inverter is working fine for your electronics. Grounds on vehicles tend to degrade over time. Like a weak 12v battery, which might seem to work effectively for the most part, but suddenly start giving strange issues, a loose or weak Ground can create havoc, too.
If that's not it, it could simply be a loose Neutral wire within one or more wiring harnesses from the outlets to the inverter, etc.