Once happened to me too, iphone 13 Pro Max refused to connect to multimedia right after i added bluetooth headphones, solved by switching to airplane mode in smartphone, and switching off bluetooth in the multimedia, then switched all back ON , never happened again (but i rarely using bluetooth headphones), in comparison with wireless Android Auto the Apple CarPlay working much better for me (sad only that google maps without voice guidance, and can't zoom maps using touch screen like in AA) .
There in engeneer menu that i used to switch Android Auto to work wireless exist menu to backup User data to USB flash drive !!!
I can`t check now if this backup working - on my multimedia usb misteriusly stopped working, now waiting for replacement.