Hide Tools overlay by script

I wish to set the Tools overlay display state to hidden by script, but I can only access the overlays in the editor window using SceneView.lastActiveSceneView.TryGetOverlay(overlayId, out var overlay)
However, I cannot find the ID for the tools overlay.
I’m able to get the overlays for Orientation using overlayId “Orientation”, but for Tools I’m not getting anything with id “Tools”.

What’s the correct ID?
Or is there a scriptable way to toggle off all overlays as possible in the overlays menu using script?