I think there are details being left out. But several people in the comments indicate that there is a Toyota app that provides various features. I bet the app implements some proprietary bluetooth service that the head unit connects to and feeds information through. Or maybe they give the head unit a straight pipe to the internet via that service.

That very much could be the case, in which case deleting the (now useless, because your car is not connected) app would resolve that - no bluetooth restriction needed.