This could be helpful for some or all. This problem was absolutely driving me crazy. My wife had the iPhone 16 (I have 16 Pro) and she also did the update to 18.4.1, but her phone connected immediately with zero problems, so we went back and forth to see what the difference could be. We spent two hours in the car trying everything while searching both English and Japanese recommended solutions without success. One of the only difference that we eventually found was Apple Intelligence. She had not elected to use Apple Intelligence, while I had it on. Unfortunately, I tried to just turn it off, but that still didn't work. With frustration, I completely reset my iPhone back to factory settings, and when I had the option to turn on Apple Intelligence, I did not turn it on. After the phone finished resetting, and started restoring my iCloud backup, I checked and the IOS was automatically installed to 18.4.1, but I went out to the car, and it immediately connected to CarPlay. IT SEEMS THAT APPLE INTELLIGENCE IS THE PROBLEM AND YOU MUST RESET YOUR PHONE TO COMPLETELY REMOVE APPLE INTELLIGENCE FROM YOUR PHONE. Note: it is possible that there is some other unforeseen problem that just resetting the phone to factory fixed, but again, Apple Intelligence was the only difference between mine and my wife's phone. Hope this helps out!