I have driven ours with the generator running several times with both coach a/c on and have not encountered the issue you're describing. I have also had the rear tank empty and was still able to run the generator, I just recently ran it with rear tank empty to help draw down the fuel level in the front tank so I could remove the fuel filler and reposition it, I went out a drove the coach with the generator running till front tank was down to 1/2.
This on a 2020 XG32, did they change the fuel system after 20? possibly, but I doubt it.
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