I am having the same exact issue with my 15 pro. Cars are 09 and 11 BMWs with retrofitted MMI box that supports wired and wireless CarPlay. The wireless works just fine, but I prefer wired connection. However, the wired connection will drop after roughly 15 seconds and my car's system would prompt "CarPlay Signal Lost" error to me. I also have a 11 regular, and the CarPlay works completely fine both wired and wirelessly. I've used multiple type C cables and adapters and still no luck with 15 pro wired connection.
Cables I've tried are: USB 2.0 speed data cable (off-branded), OnePlus Fast Charge 3.0 Cable, USB 3.0 to Type C 3.0 cable (off-branded), Type C to Type C 3.0 cable + Type C to USB-A adapter (off-branded), Ankers 310 Type C to USB-A cable, 4 in 1 USB, Type C, Lightning cable (Shezi on Amazon). And all no luck. Shezi cable is a Type C to Type C cable with a USB-A adapter on one end and Lightning on the other end, the 11 would work with all the adapters plugged in (Type A to Type C - Type C to Lightning), but my 15 pro would not keep consistent signal transfer on that same cable. Both phones are running iOS17.0.3.
Wireless carplay is not a permanent solution to me. I do not use wireless CarPlay has a noticeable delay with audio and controls, I also dislike the fact that connection stays on after I turn off ignition, and will not turn off until I lock my car. It's not as much of an issue for music, but phone calls are just much nicer to transfer to earpiece the moment the cable is pulled out.