Provide sufficient data in site backup file to re-register Joomla installed Application
With sufficient backup file (info) configuration about an installed Application (in this case, Joomla) it should be possible to "export and import" a site with a Panel installed application and have that application reappear in the Plesk server where the site is "restored". Such information is currently written to the site backup file for WordPress.
Don't necessarily need "Joomla Toolkit" ala "Wordpress Toolkit", but having sufficient configuration information about an installed application should be usable by the Plesk restore (CLI) process to restablish the previously installed application in the "new" Plesk server.
Unfortunately, we have to close your request, because over the years it has not become quite popular for further implementation.
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IG