I’m having the same frustration. Upgraded from 12pro Max to a 16Pro Max and now CarPlay does not work in my 2017 Mazda 3 GT.
called Apple support and they ran through scripts to troubleshoot only to settle on my car does not have CarPlay. Ignoring the fact that it does and that it worked in my car with my older iPhone. Two techs said this to me and the 3rd tech did a screen share and I showed them with my camera that it does have it. They said they didn’t know what the issue was with my car but offered to make it work with another car that has CarPlay.
Would appreciate help if others have solved this.