Many Cloud apps let you change the name of your current project while having it open – screenshot is from Google Sheets. I would find this handy for WS, too. That way one could rename the open project and hit "Clone". As WS is set up in a way that the current project stays active, the Clone would store your current approach. The open version would become the branch.
As a Learner I would like to mark versions when I try out something new ("version with background images"). Always having to go to the Dashboard is slow. Exploring different problem solving approaches inside one project (separate pages) means having to build a clearly labeled navigation first.
To me, it appeared most straightforward when Cloning had a Save As characteristics. Whatever you did until calling Clone would retain the current filename and would unload from the Canvas. The clone would become the active project.
I'm sure other users will differ, but I cannot imagine a use-case where I would prefer the Clone silently getting created in the dashboard.