Place element of a row above other elements to hide animation

I am trying to create a Material NavigationRail that, with the click of a button on the rail, shows a drawer with secondary destinations in my app. I have a Scaffold that as a body has a Row containing the NavigationRail and a Stack. The Stack contains the actual content of my homepage as well as the drawer, but only when the button has been clicked (I use riverpod).

I want to animate the drawer in and out on button clicks, but the drawer appears on top of the NavigationRail. How do I keep the rail in front of the drawer? If I include it in the stack, the content and the drawer are shifted to the left, behind the rail, so that does not work.

Currently, the animation looks like this:

I made a Dartpad that reproduces the behaviour: DartPad

You can use only Stack with AnimatedPosition widget.

class HomePage extends StatefulWidget {
  const HomePage({super.key});

  @override
  State<HomePage> createState() => _HomePageState();
}

class _HomePageState extends State<HomePage> {
  bool drawerOpen = false;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
        body: Stack(
      children: [
        AnimatedPositioned(
          duration: const Duration(milliseconds: 200),
          left: drawerOpen ? 64 : -300,
          width: 300,
          top: 0,
          bottom: 0,
          child: const SizedBox(
            height: double.infinity,
            width: 300,
            child: ColoredBox(color: Colors.blue),
          ),
        ),
        Positioned(
          left: 0,
          top: 0,
          bottom: 0,
          width: 64,
          child: NavigationRail(
            backgroundColor: Colors.deepPurple,
            leading: IconButton(
              icon: const Icon(Icons.menu),
              onPressed: () {
                setState(() {
                  drawerOpen = !drawerOpen;
                });
              },
            ),
            destinations: const [
              NavigationRailDestination(
                  icon: Icon(Icons.abc), label: Text("A")),
              NavigationRailDestination(
                  icon: Icon(Icons.ac_unit), label: Text("B"))
            ],
            selectedIndex: 1,
          ),
        ),
      ],
    ));
  }
}