how to pair my iPhone 13 pro to my car?

For CarPlay use a USB to lightning cable - it just works

For Bluetooth enable bluetooth pairing in the car and then select the device from the list of available devices in settings>bluetooth - remember to allow syncing of contacts etc when prompted.

Refer to the owners manual for your car which will have a full section on how to pair a phone with your car system.

Who connected your 8?

If your 8 was connecting without plugging anything else in it was paired via Bluetooth. The best thing to do is remove the pairing of the 8 from the radio in your car, then get the manual and go through their instructions for a new pairing.

It depends on your car. Did you have a phone previously connected to your car? Does your car have CarPlay? Bluetooth?