This is only about remote access, which is something that you should not care about at this stage. Try first to transfer the server data to the new machine and ensure it’s working correctly so far.
Did you copy over both the plex data folder AND the registry data?
If you did, then the two servers share a common identity.
You need to untangle them first, so they become individuals.
See Moving/Cloning Metadata - #4 by OttoKerner
After you did that, you can go and reset your client apps to use the new server as their default. It involves resetting and re-populating their left side bars with the libraries of the new server.
https://support.plex.tv/articles/customizing-the-mobile-apps-2/#reset
https://support.plex.tv/articles/customizing-the-apps/#reset
https://support.plex.tv/articles/customizing-plex-web/#resethome
