I want to backup my Genre tags from one server and restore them onto a new server

The only thing you could do is to:

‘clone’ your server,
Thereby making sure that all media files are available on the new server under the same address/path name/drive letter as they were on the old server.
https://support.plex.tv/articles/201539237-backing-up-plex-media-server-data/

I strongly recommend you to clone the server onto the same platform/operating system type.
Crossing platforms (e.g. Windows -> Linux) is only for advanced users and requires additional editing of the database.

After you have cloned your server, edit the ‘advanced server config’ of the clone
and remove the following keys:

  • AnonymousMachineIdentifier
  • MachineIdentifier
  • ProcessedMachineIdentifier
  • PlexOnlineToken

On the new server, you can afterwards delete all those libraries which should only remain on the old server.

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