I'm on a Mac so I can't testify to any issues on other OS', but I wouldn't think they'd be different as the add-on doesn't use many APIs.
Here's what I'd try:
Is your normal copy-and-paste working within Waterfox/Firefox, e.g., if you copy from some web page and then paste into the Waterfox/Firefox search bar? If that is not working, it seems it is a bug in Waterfox/Firefox, or somehow the clipboard has been disabled or for that program.
If copy-pasting in that step does work, then now try appending with append-to-clipboard context menu items and pasting the result into the Waterfox/Firefox search bar. If there is no change from your previous clipboard, my add-on (or the Firefox add-on code on which it relies) may be to blame, so I'd check whether there are any console errors (Tools->Developer->Browser console). (I do see two errors when I click on my add-on, but they seem to have no effect, and the errors seem to be from other code besides my own.)
If appending within Firefox does work, then try pasting into some other program. If that works, It may be an issue specific to your program receiving the clipboard. If it doesn't work, I assume Firefox has an issue sharing its clipboard.
I added the extension first to home-built Waterfox Classic 56.2.14 (20191007063316) then to Firefox 70.0_3,1 on FreeBSD-CURRENT.
The context menu items are present, and appear to be usable.
However, when I Control-V paste to e.g. a window of Geany (a text editor) there's either:
PEBKAM? I must be overlooking something basic …