Upverter is even unable to import something that it just exported

  1. Export your project to .upv
  2. Import it while creating new project
  3. Enjoy your frustration

That feature has been broken for at least a year.

You can fork a project if you want to create a copy of it. If you are trying to move the design from one organisation/user to another you need to make it public do the fork and then make it private again.

And with this being broken there is no way to backup your designs.