I figured out a way to reassign Ctrl+Shift+N to New Private Window using the ShortKeys add-on. I cross-posted the following from another similar question I just answered.
This add-on solves this problem in 90% of scenarios:
It allows you to create your own custom keyboard shortcuts -- and among those, you can finally invoke a blank New Private Window pressing Ctrl+Shift+N. It is able to override Firefox's own powerful Undo Close Window (a command which raised the question author's eyebrows, and still remains available just a right-click away) -- and finally makes this combo work just like it does for New Incognito Window in Chrome/Edge/Chromium-based browsers and also similar to its equivalent in Apple Safari.

Limitations: THE NEW SHORTCUT ONLY WORKS IF YOU ALREADY HAVE AN ACTUAL WEBPAGE LOADED.
Due to Mozilla Firefox's own "security" measures, it does NOT work on any of the "about:" or internal pages (about:blank, about:newtab, etc.), as well as on a new tab, empty windows, downloads/bookmarks manager, pop-up, etc.; as I type this, I also realized it does not work if the cursor is in an active text input field -- I have to click the empty blank area of this webpage first, and only then Ctrl+Shift+N will work.
Another limitation: I'm using Firefox on Windows, and I tried assigning Mac-inspired shortcuts such as Ctrl+, (comma) and Ctrl+. (period) to Open Settings Page and Open Extensions Page respectively. No idea why, but that didn't work, sigh (I was able to create these and more for Chrome/Edge for Windows with the extension Keyboard Shortcuts though, for anyone interested).