(As usual, when I ask a question I find the answer 5 minutes after that.)
It's in the lower part of the settings, called "Include MIME actions":
By default in Firefox the "normal" behavior of showing the list when copying a URL is absent: the clipboard settings have an exclusion list for the actions per window, and most browsers were listed there under Configure clipboard (right-click the tray widget) -Action menu - Exclude windows:
Most browsers are listed there, only they ignored this setting for some reason, but not Firefox; apparently their WM_CLASS name was not entered as required, but Firefox's was.
The answer here was to remove from the list the entries
Navigator and firefox.
That exclusion list is very useful if you want to stop that list from appearing only is some applications, like Dolphin (where it serves little purpose by popping up when copying a file, and that in order to provide basically the same entries as the already present "Open with" menu).
To effectively add an application to the list, run the command xprop | grep WM_CLASS and click the window of the specific application. This gives the correct form of the application name to be added to the list. For Dolphin is simply dolphin.
It must be noted
Before finding about that blacklist, I have used this workaround: enable/associate a shortcut to show that list in the clipboard settings -"Open Klipper at Mouse position":
Then, after copying link in Firefox, press that shortcut and the list of clipboard actions should appear.
