How to disable nautilus from handling the desktop?

I found that running gsettings set org.gnome.desktop.background show-desktop-icons false instantly disabled the desktop icons.

You should remove the file /etc/xdg/autostart/nautilus-autostart.desktop (or at least modify the OnlyShowIn line into it).

Then you should always run nautilus with the --no-desktop option (this could also require to modify some menu item or quicklist).

You can manage the desktop with nautilus again at any time launching nautilus without the option --no-desktop.

To manage the desktop in an alternative way you could look at some other file manager.

If you install the gnome tweak tool (which you'll want anyway) you can disable file manager handling the desktop (see Picture). But as far as I know you will then have no desktop icons. Most if not all DEs are structured such that the file manager handles desktop icons.