Please leave all Synology-related remarks aside for now. They are not relevant to the task.
So what you want to do is to copy your current Plex server data from a Windows PC onto a new Windows machine, but you may want to keep the old machine in service – so you end up with a total of 3 active Plex servers. Did I get that right?
You can perform the steps in Move an Install to Another System | Plex Support
but you need to modify them a bit.
DON’T START the server yet!
After importing the registry file, you need to open regedit.exe and navigate to Computer\HKEY_CURRENT_USER\Software\Plex, Inc.\Plex Media Server
delete those values:
AnonymousMachineIdentifier
MachineIdentifier
ProcessedMachineIdentifier
delete those too, if present:
PlexOnlineHome
PlexOnlineMail
PlexOnlineToken
PlexOnlineUsername
edit the value
FriendlyName and change it to something distinctly different than your first server
if present, edit the value of
secureConnections to be 1
Go to the Plex data folder of the new machine, dive down into the subfolder Cache and delete the file cert-v2.p12
Determine the local IP adress of the new Windows machine. (you can find it in the properties of the network connection the Windows control panel)
Open a web browser in “privacy” or “incognito” mode.
Open the adress http://xxx.xxx.xxx.xxx:32400/web
(replace xxx.xxx.xxx.xxx with the actual IP adress which you determined before)
Sign in to your Plex account and wait a few minutes, until you are prompted to “claim” the server.
Make sure to use a web browser without any “filtering” add.ins.