Honda EU2000

See what a volt meter reads at the generator. At 14 years of constant use, this gen has done its time. If it was me I’d sell that gen to someone willing to fix it and put that money towards a new one. Harbor freight and craftsman have very similar models that are cheaper and better than the Honda. To me its not worth the risk of starting a fire and possibly putting my rv and family in harms way. That’s just me though. I overthink everything.

I agree with Scott. Loose outlets connectors which is getting hot and melting things

Odd. That's usually the result of drawing too many amps, and if that were the case you'd hear the generator running very hard and loud.

Post should be moved to tech issues.

Replace the outlet on the generator with a 30 amp RV plug.

Suonds like the Honda's outlet is worn and no longer has sufficient tension. It looks like a normal receptacle so I would get either an "industrial" or "commercial" rated outlet form the HW store and replace it. I would NOT use a cheapo $.99 standard outlet.
BTW, both sides of your adapter are 110V.