I had one of the carplay units fitted ('professionally') to our F31 - it was a piece of shite. One of the issues was the reversing camera was sending 12v down to the reverse lights, meaning that once the camera was engaged, the reverse lights stayed on - even when you were driving forwards. Had the unit removed completely and got a refund, eventually. I would suggest disconnecting the reverse camera as a starting point in case its causing any issues. It does look like its a connection issue - but if you've checked everything thats not going to be it.
This looks like a similar issue - https://www.e90post.com/forums/showthread.php?t=93337