Same question here
While the overlay is active, you can simply hover the mouse over the controls. A titlebar will show, which you can use to drag the small window to a new position. Once you move the mouse away from that window element, the title for that window element will disappear too. This works for all windows, not just the record button window element.
To my knowledge, it is not possible to actually hide the recording toolbar once you start recording. Closing will end the recording.
This is what you see when you start to record from the game overlay (Win+G). Notice the grayed background showing as the overlay is active.
In the overlay, if I hover the mouse over the recording window, notice how a titlebar becomes visible with an X button. You can drag this window to anywhere on the screen to alter its location, and it will stay there when you Escape out of the XBox Overlay.