Rated 5 out of 5 stars

A button for "New Private Tab" would be awesome.

Also, it would be nice if this addon had its OWN UI with search functionality so that I could search for actions/buttons and then this extension would add them to my bars. Manually scanning through 100 actions with an arbitrary sort mode is quite an ordeal.

Edit: yes, I meant "New Private Window". Thanks! I've found the button.

This review is for a previous version of the add-on (1.0.2.1-signed.1-signed). 

I have it from a Firefox developer that due to how Firefox works a "Private Tab" is not possible. Only private windows, and there is already a button in Firefox to do that. So sorry I can't at this point possibly do that for you.

As to doing a search UI, I am planing on doing that, but I would likely put it in separate extension. For now, I also have a tool for creating versions of the extension with just a selection of the buttons in it https://codefisher.org/toolbar_button/toolbar_button_maker/