It's a while since I used Airplay for anything other than Youtube videos, but here is how I thought it worked:

1. If I choose to Airplay from the control center, it mirrors the whole screen (or possibly also extends as a second screen). Whatever I open on the iPad (or drag to the second screen) is what the audience sees.

2. If I Airplay from inside an app with presentation mode, it works similar to Airplaying a video. That one app remains active even if I switch to another app.

3. To switch what gets presented, I simply start a new Airplay session: from control center if I want to switch to sharing the whole screen, or to another app if I want that app's presentation mode. This doesn't have to be automatic, but I shouldn't have to actively close the old session to start a new one.

4. To switch back to a previous presentation, I open that app back up and re-enable Airplay - there could be a button to "resume presentation".

Maybe I'm missing something, but I don't see how that is too complicated. It seems rather intuitive that if I'm sharing a specific app window, I didn't mean to share the whole thing. (And it's also intuitive that if I actively start a new share, that takes over from the old one. No need to actively close the old share first.)