Sounds lik a compatability issue with the car. There's things to try here How to Fix S10 Bluetooth Issues with Top 7 Solutions 2020 (tenorshare.com)
I would try method 4, firstly.
Thank-you very much for the link, I have tried all of the suggestions in Part 2 but unfortunately still have the same problem. I have also tried to pair the phone with the hands free system in my wifes car but it just times out during the pairing process.
There are several Android 11 phone users who are going through the same situation (Android 11 Bluetooth issues). But, if you are one of them, you don't have to worry, just try the fixes mentioned in this post: https://recover-androiddata.com/fix-android-11-bluetooth-issues/