I’ve discovered that it will, in fact, respond to right-clicks — but only if the right-click is delivered by a two-fingered click on the trackpad, not by the alternative ALT+click method which works in all other apps I’ve tried.
This applies to the Flatpak, the AppImage and the AppImage for LibreOffice Still (7.0.x) as well as 7.1.4. It also applies on a Mac running LibreOffice Still on MacOS 10.15, where Ctrl+Click is not recognised.
I conclude that, for some reason, LibreOffice now gets its right-clicks by a different mechanism that only recognises a two-fingered click on the trackpad as a right-click, not a (special key)+click method. LibreOffice 6.4 running on MacOS 10.15 does work correctly, so the change was probably introduced in the 7.x series of LO.