How can i blur the lower layer of my windows app in Flutter

Question

In Flutter, it is easy to use BackdropFilter to blur a image or something that is a child widget of the app. But, is there any way to blur the "lower layer" of my app? Just like the weather panel in win11, the frost glass's background color changes when the desktop's color changes.

I tried

@override
Widget build(BuildContext context) {
  return Stack(
    children: [
      BackdropFilter(
        filter: ImageFilter.blur(sigmaX: 10, sigmaY: 10),
        child: Container(
          color: Colors.white.withAlpha(127),
        ),
      )
    ],
  );
}

but it's not my expectation.