Nah, I don't think they're tripping anything. In my car, my iPhone 14 Pro Max won't charge on the charging pad. The cars coil in the charging pad, isn't aligned with the MagSafe charging coil on my phone. But I can immediately place our iPhone 14 Pro on the mat and it charges just fine. It's an alignment issue with the coils. The same is true for older Qi charging stands from a couple years ago.
And yes, you should NEVER plug it in to use CarPlay while also placing the phone on a charging pad. Besides, when plugged in for CarPlay, the phone is already charging via the cord.