Download and re-publish to a different repository is unfortunately still the way to go I'm afraid. There's an idea to make this easier: Copy/Move workspaces to other repository, if you vote for that it'll increase the chance of it being implemented.

There should be a way to do it via the Rest API if the workspace is really simple and doesn't use anything difficult like a custom transformer, web connection etc. From the Rest API documentation (/repositories/< repository >/items endpoint, Publish a single item to a repository

Publishes a single item to a repository. The file name must be specified in the 'Content-Disposition' header. Note that this endpoint does not support the following: Publishing data files, custom transformers, database connections, web connections, or packages associated with workspaces. To publish workspaces to FME Server with support for any of these features, use the "Publish to FME Server" wizard from the FME Desktop Workbench. For more information, see "Publishing to FME Server" in the FME Desktop Help.

Thanks, I voted for it. Looks like it has been in the idea space for 6+ years, hope they implement this idea someday.