I found solution. Problem was in UIScene when appliaction did to background. AVPictureInPicture need during activation also active UIScene.

I changed Observer to uiSceneWillDeactivate where I activate PiP

NotificationCenter.default.addObserver(
    self,
    selector: #selector(uiSceneWillDeactivate),
    name: UIScene.willDeactivateNotification,
    object: nil
)