Thanks @nephros.
So last week it suddenly worked for two days and now does not work any more. Under “Show device settings” and “Type” I have “Car kit” selected. But what I have noticed is that if I click on “Type” while connected to the car “Headset” is the option that is highlighted (and changing it has no effect). Disconnecting and then connecting again from the phone after selecting “Car kit” has no effect. I will try disabling BT and enabling it again, I am not sure if I have tried that particular approach. If I disable “Always allow connections from this device” and manually connect from the phone every time would that help I wonder? I don’t remember if I already tried that either.