It would be nice, in addition to Save as New Version, to be able to save the current opened project, as a new Template so that it appears in Templates, since we can manage templates created by the developers but not very easily our own, without having to interact with the file system.
Since your feature request matches exactly the currently available functionality… are you missing something about the current “Save as template”?
Indeed, this feature “save as template” the current project is older than me. I use it all the time and I think I have never used a “factory” template, maybe for testing little things, but not for my projects.