We're having this same problem with a 2022 Honda Civic Sport sedan. Wired CarPlay using a USB to Lightning cable, with the Lightning to USB C adapter on it. All are Apple cables/adapters.
All of our other iPhones work in this car with CarPlay with no problems (iPhone 11, 12 Pro Max, 15 Plus). From what I've read in about a dozen different threads like this, this is a problem only with the 15 Pro models.
We'll begin the hunt for a direct USB A to USB C cable (no adapter) today to see if that fixes this problem. If that fails, then we'll have Honda update the head unit if possible. If that all fails, the 15 Pro Max goes back to Apple to be exchanged for the 15 Plus because it's not practical in my son's job not to have a navigation system in the car.