The preferences file contains a number of „machine identifiers“. Those will have changed during the reinstall of your Mac.
- stop the Plex Media Server
- remove the various machine identifier properties from the preferences (see: Plex not finding libraries after restore from time machine and Big Sur update - #9 by Volts)
- restart your server
I don’t remember if this will require your server to be reclaimed but it should be fairly straightforward from there.