Teddy Svoronos:
As of iPadOS 27, if you have multiple windows open while AirPlaying (whether or not Stage Manager is on), tapping on anything other than the presenting app will snap the external display into showing your whole iPad screen.
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As for what the behavior should be, I’m not a developer, but here’s a proposal: if you’re using an app that is in presenter mode (e.g., PowerPoint playing a presentation, or a GoodNotes document open), it should always get precedence on the external display, until that presentation gets stopped, the document is closed, or the app is quit. Period.
This is extremely annoying, and fixable. Teddy’s proposed fix is the right one.