iOS 14 introduced a system notification when an app pasted from the pasteboard as a security feature. In iOS 15, Apple is introducing "secure paste", which seems like it will bypass this notification when the paste is initiated by the user.

https://www.apple.com/newsroom/2021/06/apple-advances-its-privacy-leadership-with-ios-15-ipados-15-macos-monterey-and-watchos-8/
https://developer.apple.com/videos/play/wwdc2021/10085/?time=360

That information about the feature is vague, but it may not be possible for Flutter to implement this, at least for the text selection menu, since Flutter doesn't use the native text selection menu. If I'm understanding it correctly, tapping on Flutter's "paste" button will always be treated as being initiated by the app, and it will show the notification.

We may be able to support this for the keyboard by receiving whatever "user paste" event Apple creates and sending something along to the framework.

CC @jmagman