The reason behind this change in experience compared to older Ubuntu releases is that the GNOME developers have relieved recent versions of Nautilus (aka (GNOME) Files, the default file-manager application) from handling the the desktop and the items on it. The rationale behind this decision can be found here: https://gitlab.gnome.org/GNOME/nautilus/-/issues/158. The standard unmodified GNOME desktop comes without the desktop icons feature altogether.
To mitigate the issue, Ubuntu developers have shipped Ubuntu 20.04 LTS (in fact, it's happening since the Ubuntu 19.04 release) with a GNOME Shell extension called 'Desktop Icons' (package name:
gnome-shell-extension-desktop-icons) which handles the desktop and provides the desktop icons. But currently the extension offers only a limited set of features, so you would find many of the standard desktop features missing.
A workaround would be to use a different and slightly more featureful extension, called Desktop Icons NG (DING) by Sergio Costas (a fork of the Desktop Icons extension). Note that you need to disable the pre-installed Desktop Icons extension first (using the 'Extensions' application, for example).
Desktop Icons NG (DING) offers some extra features compared to the default one, for example
- Drag-and-Drop, both inside the desktop, between desktop and applications, and nautilus windows.
- Allows to use the 'Open with...' option with several files.
- When hovering or clicking on an icon with a name too large to fit, it shows the full name.
- Usual keyboard shortcuts to cut/copy, paste, select all, delete (both move to trash and delete permanently).
- Option to show a 'delete permanently' action in the context menu (right-click menu).
- Option to show removable drives and network drives on the desktop.
- Option to choose alignment for new icons.
Refer to this to learn more about installing and configuring GNOME Shell extensions: How do I install and manage GNOME Shell extensions?