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Since it sounds like your phone is allowing access, I would try fully deauthorizing the Bluetooth connection between your phone and the car and make sure to click "pair" on the phone first thing when the prompt comes up.
If you don't get a notification on your phone saying "allow access to contacts" during the reconnection process immediately go the advanced settings and check the box shortly after.
Hopefully it resets the connections and authorizations as long as your cell is relatively* new.