Similar issue here. 2014 Ford Fusion. Bluetooth has always worked flawlessly with my car. I updated to 16.4 on 4/4/23 and that same day my iPhone disconnected from Bluetooth in my car. I have rebooted the phone and car system, completely forgotten and re-setup the device again multiple times. For me, the iPhone (mine’s a 12 Pro Max) will connect and then almost instantaneously disconnect. I don’t even get 30 sec of music like the OP. Fix this Apple!