I’ve never seen any documentation that extension cords are prohibited, though iirc the FAA does have some standards for cords (have to be controlled so they don’t impede passenger movement, etc.) I’m interested in a definitive answer as well. If AA has such a policy, it’d have been FAA approved - but I’m unaware of one. Unprofessional FAs, I’m aware of. Fortunately, they’re relatively uncommon IME,

Tangentially, the US twin blade and even the two pin Euro portion of plug receptacles on aircraft are often well used and the plug will attach loosely. My answer has been a simple UK to universal plug adapter, which is relatively small and usually fastens solidly into the plug receptacle.

I’ve never had any problems with this in aircraft cabins.