I think the reason the control panel is not being positioned properly is that in immersive mode a new camera is activated. I tried to figure out which camera is being used and use the position and rotation of that camera to position the control panel but I was unsuccessful.
I have not figure out effective methods of debugging, like using the inspector, in immersive mode. Yet.
WebXR doesn’t support fullscreen UI. It is technically possible (though not yet integrated), but makes little sense, unless you want to display HUD-details. You can’t interact with a full screen UI.
The better approach is either to create a “menu”, based on a plane (for example), and attach the advanced dynamic texture to it, or use the 3D gui elements. Those can be positioned where you think it makes most sense - connected to the controller, 1 unit away of the user, as a child of the webxr camera - whatever fits the usecase.