Unable to delete libraries

You need to access the Plex data folder on your Syno. See Synology FAQ - Questions, Answers, and a few How-To's

Shut down Plex server on your Syno,
copy the file com.plexapp.plugins.library.dband (if present) its “companion” files
com.plexapp.plugins.library.db-shm
com.plexapp.plugins.library.db-wal
over to your Windows workstation.
Download the sqlite tools for Windows and repair the DB.

Proceed according to the help article.