On my Ubuntu 20.04 synaptic works fine clicking on the icon and desktop file is as follows:
Code:
[Desktop Entry]
Name=Synaptic Package Manager
GenericName=Package Manager
Comment=Install, remove and upgrade software packages
Exec=synaptic-pkexec
Icon=synaptic
Terminal=false
Type=Application
Categories=PackageManager;GTK;System;Settings;
X-Ubuntu-Gettext-Domain=synaptic
StartupNotify=true
StartupWMClass=synaptic