Great update Jon, thanks. Exciting to see what the research shows.
Interesting comments from everyone 👍
Just thought of some details. Maybe the tab itself should be blank or just not show any info about the page it contains.
Also, if the window with a private tab have been minimized. Then when opening the window again, it probably shouldn't open on the private tab. Maybe it could open on the start/home tab or a new tab.
A partial solution to this would be https://addons.mozilla.org/en-US/firefox/addon/temporary-containers/