Hello mmagr88,
We see you're having issues with connecting your new iPhone to your car's Bluetooth. We'd be happy to help.
Are you able to successfully connect any other Bluetooth accessories/devices to the iPhone? If not, try these steps: If you can't connect a Bluetooth accessory to your iPhone, iPad, or iPod touch
Be sure to check for any available iOS updates as well at Settings > General > Software Update. The latest version at the moment for an iPhone 13 will be iOS 15.1.1.
Some general other steps that can help would include the following:
-Restart the iPhone
-Go to Settings > Bluetooth (not Control Center), and turn off Bluetooth. Wait for about 5 seconds, then turn Bluetooth back on.
-Try changing the new iPhone's name in Settings > General > About > Name.
Cheers.