I have similar situation. I have Citroen C4 (B7) 2011 and my iPhone 12 Pro connecting with car as to bluetooth mode. First is audio streaming mode and is always connected and second is headphone mode. Headphone mode after 10 seconds connecting is disconnected automaticly. Even if I reconnect headphone mode then still after 10 seconds iPhone disconnect connection ehh :( This is unthinkable in 2021.