How to backup libraries, metadata, covers, etc., if I need to change my hard drive where the plex server is?

If you need to relocate you media: Move Media Content to a New Location.

Metadata, etc is stored in the Plex data folder. See Move an Install to Another System, as you’re basically doing the same as moving to a new server.

If you need more space on the C:\ drive, you can move the Plex data folder to another drive. For example, from the default location, C:\Users\<username>\AppData\Local\Plex Media Server, to E:\plex\Plex Media Server.

Details: [HowTo] An extended guide on how to move the Plex data folder on Windows