I don't think it's even possible to use gtk4 to build a dialog, as gtk4
has dropped GtkPlug/GtkSocket and doesn't support embedding anymore.
They also don't seem to give access to enough internals so I can build
it myself.
This includes an abortive attempt to do a gtk4 dialog (which I don't
think is possible, as gtk4 doesn't allow embedding toplevels anymore),
and an iced dialog, which I just never started writing.