Also remember that you can recharge the truck at any campground you might be parking the trailer at.
Maybe. Some of them outright prohibit it because their wiring can't handle the load.
A lot of posts I've seen have a TT30 on them as well as a NEMA 14-50 and they both work because one is 120V@30A and the other is 240V@40A.
Yeah, in some cases they are wired to the same circuit though. They shouldn't be, but RV campgrounds often aren't held to any reasonable standard.
I'm on some schoolie groups and may still be in rvelectricity (if I haven't been booted again for complaining about AI slop) and bad hookups at RV parks are horribly common.