Not true. You can have several servers. Plex is developed for this case.
As the linked article explains, you copy the Plex data folder to the new machine.
Make sure to use a regular NTFS volume as destination.
Do not use a volume that has been pooled or mirrored etc with Windows Storage Spaces.
Both “source” and “target” Plex servers must be stopped during the copy process.
I’ve used robocopy (several times already) with success for that.
(if the destination folder is not in the default location, you need to create a value in the registry, which points Plex server to the right folder. See [HowTo] An extended guide on how to move the Plex data folder on Windows )
Then you export the registry branch and import it on the new machine.
After doing so, you must never start the plex server on the old machine again!
You may need to perform Plex install fix for Windows Server (Claim issue) to reclaim the server.