There is a number of threads on this forum describing the same problem when a Synology NAS sees no files and subfolders in the default video folder even though all access rights seems to be correct. E.g. :
I had exactly the same issue, but found a better way to solve this without moving all media to a different folder.
Just login to your Synology via SSH and execute the followin as the root/admin:
sudo chmod -R ug=rwx,o=rx /volume1/video
(where /volume1/video the real path to your problematic folder).
The command above lets all users (the default linux group called “users” in Synology) to write/read/execute(browse) to/from the /volume1/video and all others (including plex) to read and execute (browse through the subfolders).
Obviously the underling problem is that the user rights are not shown correctly in the Synology’s web interface and the plex user in fact has no access to the /volume1/video. Removing and setting back the rights via GUI did not solve the problem in my case. Only the explicit chmod linux command did help.
I got this problem for all folders that were migrated from an old synology /volume2 to a new synology /volume1. The folders migrated from /volume1 to /volume1 didn’t have this strange behaviour for whatever reason.
Synology reserves all rights and controls access to the default video share
It is for this reason we URGE everyone to make their own share(s) independent of the default/pre-created shares. We also urge to NOT place media in the Plex share (that’s for internal Plex use only to store your metadata)
This FAQ walks through setup of Plex on a Synology.