Jumpy
Same problem here with Nemo on Solus, no icons.
When I use Nemo on Debian 11 bullseye, context menu icons show up correctly, just out of the box. org.cinnamon.settings-daemon doesn't exist there at all.
On my Debian system I created a few right-click actions in ~/.local/share/nemo/actions and it seems that only icons located in /usr/share/icons/Papirus will show up in the context menu (though I seem to be using the Papirus-Dark theme). Turns out I can use any icon from any theme in /usr/share/icons/.
On my Solus systems the globally used icon theme is set to Papirus, the Widgets to Plata-Compact. Those are settings identical to what I see in org.gnome.desktop.interface, so I assume those are actually in effect. But that settings path does not contain a setting menus-have-icons...
Could it be a Gnome problem?