(edit 5-11)
Sorry I didn't see your edit sooner.

If you open ContextSearch options, scroll down to Opening and Closing and you can choose a method to open the quick menu.

Automatic (popup opens after selecting text)
Mouse hold (hold either the left or right button until popup appears)
Mouse click (right-click to open )
Keyboad button (press a keyboard button of your choice to open)
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Does it not work on any website or just addons.mozilla.org? Mozilla disables certain add-on features on addons.mozilla.org for what I assume are security reasons. Using default settings, it should work by highlighting text and holding right-click until the menu appears ~0.25seconds.