The about:privatebrowsing page is not used on private browsing mode aka "Never Remember History".

For private windows in normal mode, the extension New Tab Override can be used (with private browsing permission) but new private windows will still show about:privatebrowsing.

The contents of about:privatebrowsing can be made blank with userContent.css.

Are you using permanent Private Browsing mode (Always use Private Browsing mode; Never Remember History) or do you use a command-line or the Windows shortcut on the Task bar? The later might make Firefox show the about:privatebrowsing page. You could try a desktop shortcut that has a space and "about:blank" appended.