Hi, Please try to Reset network settings option and see if it will fix the car bluetooth shuttering sound issue.
It allows your phone to reset Wi-Fi, Mobile data, and Bluetooth to their initial states.
Follow the steps below to reset network settings.
1.Navigate to Settings. Search for and select Reset network settings.
2.Tap Reset settings, and then tap Reset settings again.
3.If needed, enter your phone security credentials, and then tap Reset.