Sorry for the late reply. It’s unfortunately correct that this is still not supported yet, I hope we can implement such a feature soon. The cleanest way to copy a project is still Cloning a project, there's no "save as" - #6 by grubernd.
But it’s really not that bad to just copy a whole projects directory, it shouldn’t cause real troubles. The *.lpp file inside the directory can be renamed as desired.
Sounds like the hidden file .librepcb-project was not copied.