On Ubuntu, I would run the following command sudo ln -s /path/to/application.desktop ~/Desktop
And it would copy the .desktop file to the Desktop folder, which would make them display on my actual desktop. It would look like this, for example:
Desktop files and folders are not part of the Gnome DE in the sense that they can be displayed on your visible desktop. Regardless of what lies in your $HOME/Desktop folder.
Instead, Gnome uses what they call Dash.
As witten by @anon11595408 a standard Gnome installation does not have icons on the desktop any more. You have the dash where you can stick the programs you need often.
But there is a Gnome shell extension which adds this: https://extensions.gnome.org/extension/2087/desktop-icons-ng-ding/
You can install the extension via the AUR and yay too: yay -S gnome-shell-extension-desktop-icons-ng
But there are many reasons why the Gnome developers removed the icons from the desktop.