carplay vs bluetooth

I have a dual system in my vehicle - a factory fitted stereo with Bluetooth (provides telephony and music streaming), and an after-market CarPlay head unit (connects to the phone via WiFi, and broadcasts to the radio). I have the iPhone set up to connect to both devices (as the telephony from the in-car system is so much better). This has worked perfectly in the past.

I have disabled the ability for the phone to stream audio to the car stereo in the stereo itself. I cannot find how to turn that off in the phone though. When the phone connects to the CarPlay system, it insists in trying to stream music from whatever source (the Music app, radio app or Spotify) to the Bluetooth instead of the CarPlay.

in all other ways, the CarPlay system is flawless. When I had the setup in place in a previous vehicle, I didn’t have this problem - music was always played through the CarPlay as a first choice.

my question here is - how do I force the phone to play music through the CarPlay as a first choice, in these situations ?

thanks. I am using an iPhone 14 and IOS17