Phone & car are connected through Bluetooth

Go to Settings>Bluetooth, select the vehicle, and you should see a switch to sync Contacts. However that could be only half of it. Check the Bluetooth settings for the car and see if there is a separate setting in the car to sync Contacts. If you cannot find information for that, you may need to contact your dealer.

Then contact your dealer. If you are not seeing a setting for Contacts when you look at the vehicle setting in Bluetooth on the phone, then it is all controlled by the vehicle.

Have you looked when you are connected to the vehicle then? Did you check the vehicle's settings to see if it allows for syncing the Contacts? There has to be a grouping of settings for the phone when connected via Bluetooth.