isPictureInPicturePossible false on tvOS

I have picture-in-picture working on iOS, finally, because v15 introduced an initializer for AVPictureInPictureController() that can be used with an AVSampleBufferDisplayLayer.

However, using a largely shared code base (at least for the video display portion of the app), isPictureInPicturePossible is false when I try to PiP on tvOS.

My AVAudioSession is configured with .playback.

The app itself has Audio, AirPlay and Picture in Picture mode enabled in the Background Modes section.

Has anyone got PiP working on tvOS? Are there any tvOS-related requirements that differ from iOS?