I have a 2019 model LEXUS NX and paid to have CarPlay added when it became available a couple of years ago. All fine and dandy with my iPhone 12 but when I tried the iPhone 15 with its USB-C connector ..... no go as with everybody else on here. (The LEXUS CarPlay connection is wired only).
I tried several different cables along with a good quality USB-A to USB-C adaptor with the Apple USB-C cable without success until just now.
What did I do? I tried a cable which I bought from TetherTools for use for my camera. These cables are very expensive but top quality. Once I used a TetherTools cable, the wired connection was perfect. (With other cables, I either got no response or the phone kept saying it was charging before dropping the connection).
Unfortunately, the TetherTools cable is several metres long so not practical for continued use BUT having established the connection and once the iPhone "knew" the car - listed in the CarPlay settings on the iPhone - I was able to use a 'normal' cable which had previously failed to work.
Hope this helps.