Apple CarPlay works over my USB-C cable, at least in my 2018 Subaru Crosstrek on an iPhone 15. No Bluetooth required I am fairly certain. I also have to unlock the device every so often with my Face ID -- unsure what triggers this as it is not 100% of the time.
My car also uses wired Android Auto, but somehow after I set it up the day I drove it home, my phone automatically connected to it via Bluetooth. I recall something similar when a friend plugged in their iPhone but I’m not sure.
I always connect to CarPlay with a wire, and have never connected with bluetoooth. It has not auto paired Bluetooth either with iPhones.
I have not used Android Auto, but if it does auto pair Bluetooth, that would be a shame. I thought the whole point was that the car just provides a screen your phone can extend a display to, and no data ever leaves.