I am trying to create a game that emulates the windows fluent design, most of it is fairly doable with shaders but I am struggling with one problem that I cannot seem to figure out:
How can I create a blurry background that shows the stuff behind the app in a blurry way? Something like this:

Setting the entire viewport transparent is doable with
get_tree().get_root().set_transparent_background(true)
and then I tried to add a shader:
shader_type canvas_item;
void fragment(){
vec4 color = texture(SCREEN_TEXTURE,SCREEN_UV,2);
COLOR = color;
}
but the shader only shades what is in Godot itself, so it doesn't help.
I thought about using some kind of screen capture and setting that as a background texture but the problem there is that I wouldn't get the stuff behind the game but rather the game itself, so this doesn't help either.
Is there a way of doing this at all?