Similar to the "send tab to device" or "open in new container tab" in the context menu that shows up when right clicking a tab in the tab bar. or even an "open in not-private window" option in the "move tab" submenu.
right now if I want to access I page I've navigated to in my non-private context I do <c-l><c-w><m-tab><c-t><c-p><cr> which works but is a bit of a mouthful.