in GTK when you instantiate the window you pass what is called the "transient for" property (https://docs.gtk.org/gtk4/method.NativeDialog.set_transient_...). That informs the dialog what it belongs to. If you were to re-engineer this to make the file picker its own process, then you would have to fundamentally change the way it functions, sadly.

Edit: And I think Wayland would make this impossible? Someone correct me if I'm wrong here, but don't you lose basically all inter-window introspection with it? There may be some negotiation process, but I don't know how you would go about accessing an entirely separate application's context under that pipeline.