Can we name the private window start tab something other than "about:privatebrowsing"?

Thanks for the explanation. Nice catch!

Same behavior for me as before. However:

Indeed. When setting that pref I can reproduce this. When opening a new private window through the App Menu (hamburger menu on the top right), or Ctrl+Shift+P, it just opens a new “New Tab” without being in actual Private Browsing mode. This behavior is IMHO correct as Firefox wouldn’t remember history anyway, though that could also be confusing.

However when having that pref set, and choosing “New private window” from the taskbar context menu, then I can see the same as you are seeing. IMHO this should behave exactly the same as when choosing “New private window” from the App menu. Therefore this sounds like a bug to me.

Would you like to file this bug in the bug tracking tool? Here’s the link for that:
https://bugzilla.mozilla.org/enter_bug.cgi?product=Firefox&component=Private%20Browsing