How to save and restore workspace in Ubuntu 20.04?

You may have missed the final step in the equation.

The next step is to setup in Startup Applications the applications you wish to load on startup of your PC and to set up in the extension the Workspace you wish to associate the application with.

You can access Startup Applications by pressing the left windows key - also known as the Super key and in the search tool bar enter Startup and select it from there. The Configure this extension icon allows you to complete the process for the extension.

Note that in the above graphics, Auto Move Windows contains an entry for Chromium Web Browser but that is not included in Startup Applications as a result of which it does not get loaded at startup - which is directly the effect you are experiencing.