You won’t have any better luck in the support community. Support has zero clue what is causing the glitch & they aren’t even aware of how widespread it is. This issue is happening to multiple vehicle manufacturers, stock head units & aftermarket. It’s been/being discussed on multiple forums and websites also. Some people have had luck with resetting network settings and restoring a backup. This was not my experience of course. I did get CarPlay to work after erasing all settings but as soon as I restored my backup it was gone again. The restore was done with a clean ipsw but still nothing. If you’re willing to go without your backup it seems like you can get up & running. Support has tried to be helpful, but to be honest running me through how to reset CarPlay wasn’t doing much. They did say they’d try and get back to me by Tuesday though…yay! Just like the OP my iPhone 11pro running iOS 15 with the same build number has zero issues with CarPlay. I’ve literally done everything. This is an Apple issue. Good luck, if you find a fix that allows you to keep your info please update us. I’ll do the same.

I haven’t actually tested this yet but I’ve seen several tweets saying the bug appears to be linked to the equalizer in the music app, possibly even more specifically to the late night setting. The posts I saw all said turn off the EQ, several mentioned the late night as the setting they were using prior to shutting it off.