Can't access control center or a different desktop while using AirPlay(video).

Currently it appears in MacOS 13, when an end user is using AirPlay to play an video from an app on an iPhone, the screen becomes full screen and end users are unable to open control center or swap out of the fullscreen mode by swiping left, right, up or even using the control buttons and left right and up buttons.

It would be nice to use my code editor while using AirPlay since the videos don't work well or at all on udemy website with audio on safari. (whole different issue, probably Udemy's site issue)

If this is not a bug and the current feature is as designed to stay full screen until exiting out, can I make a suggestion and allow this feature to be controlled as it is in safari with full screen videos?

I feel limited and I've heard that this works if I have another monitor but that seems to limit the features within the macOS software for end users that do not have an separate monitor or display hook up.

End goal would be to be able to pause or even keep the window open while using a different program like a code editor within a different virtual desktop, or allow users to return to their main desktop without having to pause. exit out of full screen (which kills the stream), and then recast the video to the MacBook.

Picture in Picture mode would be nice as well for airplay.

Thank you, and if there is a better place to add these suggestions please let me know.