You will be much better served by placing your media in a shared folder that is not in a user home directory. It avoids the permissions issues you are experiencing.
A straightforward method is to make a shared folder such as /media, with subfolders for movies, TV Shows, etc., then give Plex Media Server read-only or read-write permissions to /media and all subfolders. This gives Plex access to the media and avoids Synology DSM changing permissions and causing problems for Plex.
See FAQ 6: Recommended Media Organization and Adding Media to Plex and FAQ 29 - DSM 7 - Give PlexMediaServer access to your media.
