(In reply to Joanmarie Diggs from comment #6)
I think one should be able to interact with all the push buttons on either side of the location bar in Firefox without having to use flat review or a mouse to click on stuff.
This is now possible. See bug 1436086.
(In reply to 166291 from comment #12)
I tested this with another extension earlier (uBlock Origin) and found that while I couldn't focus the elements within the popup, if I opened the moz-extension://.../popup.html in another tab I could focus the elements using tab
When you press the button to open an extension popup, the popup should get focus automatically. I haven't tested this with these specific add-ons, but it works here on Windows with Lastpass and Tampermonkey. I'll have to try this with the add-ons you mention.
Can you please try this with the new toolbar keyboard navigation in Firefox beta or nightly? Focus the address bar, tab to the Library button, then use the right arrow to locate the button for your extension and press space to activate it. Does anything get focus when you do this?