This happens every time I get a new phone, each time with subtle differences. This time it is with the Galaxy Fold 3 (nice phone but a PITA to have bouncing around in your pocket). In the Jag it will drop out after a few minutes after startup for a minute, then reconnect, then drop out again after another minute or two, and reconnect - about 3 - 4 times. a real nuisance when you are on a call, worse if you are using spotify because the volume has to be right up for it, when you get a dropout it switches to USB or radio and blows your eardums out.

Anyway this one luckily seems to have been corrected by a software update in the car, our IT fellow suggested that the car will be on a very old version of bluetooth whereas the phone is on version 5.2, I can recall rolling back the bluetooth version on a previous phone to fix connection issues but that was probably 3 versions ago.

So anyway short answer is that for the incontrol with the hard side buttons, a software update done by Jag seems to fix the issue.