I'm an owner of a Ferrari Roma MY2021 and Lamborghini Aventador S Roadster MY2020 and have suffered this problem for weeks since I bought a new iPhone 15 Pro on the day it launched. Because I haven't updated the software of the Ferrari, neither of the two supports Wireless CarPlay, so I was in the same situation as you and had to fix the problem.
Long story short, the problem was the cable and both works well with the USB-A to USB-C cables. I mean, iPhone 15 Pro x Ferrari and iPhone 15 x Lamborghini. Guess the cables i'd tried before were charging only (not transferring data). Had bought Belkin USB-C to USB-A Cable (it says it is a 1M, 3.3FT, 10Gbps USB-C 3.1 Cable. Can't find SKU number, sorry.) before I read this thread, and bought the recommended Anker 322 USB-A to USB-C Cable 6ft Braided. Both work fine. Moreover, I came to know that my Aventador supports Android Auto. I tried connecting my Galaxy ZFold 4 with the Anker cable and the Android Auto showed up. I'd thought the car doesn't support Android Auto before. In contrast, Roma didn't support Android Auto.
Someone in this thread said they felt the sound quality also got better after changing the USB cable. It could be a sort of placebo, but I felt so too, anyways.