You are not importing a backup of the registry keys at every backup? (Just checking – you should NOT do that.)
Is there perhaps any other software on your system which aims to revert registry changes? (some kind of “hardening” software or a “kiosk” solution)
Take a look at the default location ofg the Plex data folder (i.e. on drive C:)
There should be a preferences.xml file in there. Open it with a text editor and see what it contains. It should only contain two short lines of text. In particular it should NOT contain any hints at the location of the plex data folder.
Now look at the same-named file in your new Plex data folder location.
It should contain much more data. But also NOT the key LocalAppDataPath.