Hi!
I am using now miui 13.0.9.0. Music control is available when you activate the small screen by double tap (so you turn the screen to show you, as default, the hour) and then you just have to swipe from the bottom to the top of the screen, the music player should appear.
If it doesn't, I would delete the data of the rear display app (you can find it in apps list, but it's a system app so choose the option to see system apps) and then configure the settints of the rear diaplay again.
About the apps notifications, it was never working for me. I don't know how to set it up.