When you get a chance, try forgetting the remembered Bluetooth connection and re-pair the iPhone with your car to see if that changes the behavior. Also, do you know if the new car is CarPlay enabled? If it is CarPlay enabled, try connecting it that way to see how that goes:
Use CarPlay with your iPhone
Since the issue only seems to happen with your vehicle and not other Bluetooth devices paired with your iPhone, it seems that the issue might be with the Bluetooth signal being output from the car stereo. We would recommend checking to make sure there aren't any firmware updates available for your vehicles car stereo.
If you need additional support beyond that, we would advise reaching out to Apple Support directly using the following link: Get Support
Cheers.