WARNING: Usually the method below is not recommended at all, but you can continue if you really want to get ScreenLets installed on your system.
This method is an adaption of method for 19.04.
We need to add Ubuntu 16.04 LTS repositories to the system:
cat << EOF | sudo tee /etc/apt/sources.list.d/xenial.list
deb http://archive.ubuntu.com/ubuntu xenial main universe multiverse restricted
deb http://archive.ubuntu.com/ubuntu xenial-updates main universe multiverse restricted
deb http://archive.ubuntu.com/ubuntu xenial-security main universe multiverse restricted
EOF
Then we need to install LibPNG 1.2 from linuxuprising PPA (as the regular deb-based method does not work):
sudo add-apt-repository ppa:linuxuprising/libpng12
sudo apt install libpng12-0
Then we need to add ScreenLets PPA:
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv 94E58C34A8670E8C
sudo add-apt-repository "deb http://ppa.launchpad.net/screenlets/ppa/ubuntu xenial main"
And finally we will be allowed to install ScreenLets:
sudo apt-get install python-gobject python-gtk2
sudo apt-get install screenlets-pack-all
and enjoy.
To prevent possible problems with packages from 16.04 LTS you have to remove its repositories from the system with:
sudo rm /etc/apt/sources.list.d/xenial.list
sudo rm /etc/apt/sources.list.d/xenial.list.save
Note: just tested this method to install ScreenLets on Ubuntu MATE 20.04 LTS. Not sure about GNOME Shell.