If you have not already, read Installation & Setup of Plex Media Server on Synology. It will help with running Plex Media Server on your Synology NAS.
Edit: The version of PMS in the Synology Package Center, 1.18.5.2309, was released in January 2020. Consider manually updating to the current version. The “Installation & Setup” document has information on how to manually update. Also see the Synology FAQ #2 and #3.
To directly address your issue:
Make sure the plex user has at least read only permissions to the media files. See Synology FAQ #19 for details on setting permissions.
Also review how you have the media named and organized.
For best results, follow the Plex recommendations as close as possible. See the Your Media support documents. Plex is very picky with TV shows, so follow those recommendations explicitly.
