Repeating error: Can't install desktop-icons@csoriano

I ran into the same issue, and fixed it by manually rebuilding the desktop-icons@csoriano folder using their git repository.

Apparently you cannot really remove desktop-icons@csoriano and other extensions in /usr/share/gnome-shell/extensions/ from the system. They are expected by Ubuntu 20.04 to exist globally. It seems to me like their changes can only be actively overwritten by other (global and local) extensions. Another approach whould be rebuilding a "modified" version of the extension that simply does nothing.

Here are the steps to fully reconstruct the original /usr/share/gnome-shell/extensions/desktop-icons@csoriano/ after deletion:

# Corona-like I stayed at home for this. You can also do this in another location, doesn't matter much for the following steps...
cd ~
# Install the building tools used by the makers of desktop-icons@csoriano
sudo apt update
sudo apt install meson git
# Clone their repository to ~/desktop-icons/.
# MAKE SURE there is no file or directory in home called "desktop-icons"!
git clone https://gitlab.gnome.org/World/ShellExtensions/desktop-icons
# Enter the cloned repository.
cd desktop-icons
# Prepare building the extension using meson.
# This will set the location of the build in it's config. So even if /usr/ is a root location, we don't need sudo for now.
meson --prefix=/usr/ --localedir=share/gnome-shell/extensions/desktop-icons@csoriano/locale .build
# Build the extension. You can execute this using sudo, otherwise you'll be asked for the root password by ninja.
ninja -C .build install

# We're technically done. Now let us clean up what we needed for the above.
# Remove the cloned repository.
rm -rf ~/desktop-icons/
# Remove building tools. You can keep these packages if you like, but they aren't needed for the extension anymore.
sudo apt remove meson git
sudo apt autoremove

# Apply changes (you might do that after you continued reading this post to the end).
# Alternatively you can just restart gnome, for that see https://stackoverflow.com/q/46565019/7638119
sudo reboot

For more information and if you got in trouble while following these steps, visit the official repository and maybe their issue page.

Here are the steps to modify the extension so that that it simply does nothing:

cd /usr/share/gnome-shell/extensions/desktop-icons@csoriano
# empty its entry script
sudo mv extension.js extension.js.old
sudo touch extension.js

(This might causes issues in future updates of Ubuntu 20.04. To undo this modification, just run cd /usr/share/gnome-shell/extensions/desktop-icons@csoriano; sudo mv extension.js.old extension.js.)

You mayhaps got in this situation because you followed the official workaround to fix the Ubuntu 20.04's desktop icons by installing nemo alternatively, like I did. I highly recommend you to undo this and wait for an official patch. Updates on a patch can be seen here on launchpad.net. Other workarounds can be seen there as well.

If you want to uninstall nemo and wait for an official patch of the issue, do the alternative installation in reverse:

# Remove nemo from local autostart.
rm ~/.config/autostart/nemo-autostart-with-gnome.desktop
# Remove the nemo package.
sudo apt remove nemo
sudo apt autoremove

# Apply changes.
# Alternatively you can just restart gnome, for that see https://stackoverflow.com/q/46565019/7638119
sudo reboot

**** In "Software and Updates" i enabled (main),(Universe),(restricted) and (multiverse)*** it need universe package to be enabled , you can disable it after installing if you dont need it

Solution 1:: Try reinstalling using command

sudo apt install gnome-shell-extension-desktop-icons

Then Reboot..

Solution 2:: Try removing package first if it's installed and not working using

sudo apt purge gnome-shell-extension-desktop-icons
                      or
sudo apt remove gnome-shell-extension-desktop-icons

then do install again using

sudo apt install gnome-shell-extension-desktop-icons

Then Reboot.. Hope This Help

But this extension causing problem when drag and drop from desktop so if you need drag and drop from desktop uninstall it and use the extension https://extensions.gnome.org/extension/2087/desktop-icons-ng-ding Dont forget to reboot after removing extension using

sudo apt purge gnome-shell-extension-desktop-icons
                   or 
sudo apt remove gnome-shell-extension-desktop-icons

For me installing gnome-shell-extension-desktop-icons-ng is what fixed it for me.