In both my Kia Niro as my Hyundai Ionic 5 I need to connect via USB for AA to work. Even have to use a specific USB port in my car, only 1 will work with AA. That seems to be a choice car manufacturers make.
I also had problems with sudden disconnecting and reconnecting. When it got worse, I noticed that my charger cable at home also frequently disconnected. Solved it by replacing the bottom module of my FP3.
I get this too. To avoid it I have to carefully place the phone in my Peugeot so the cable does not work loose. When I had an FP2, there was a metal housing around the microusb port which could be squeezed a little to hold the cable firm but no equivalent in the FP3
Also noticed having to reinsert charging cable at home. Giving a very slight squeeze to the plug on charging cable has made this completely reliable again. I get that this might not work for all however.