Synology DSM7 - Plex No Longer Finding New Files

Please turn off verbose logging. It causes the log files to wrap too quickly.
SettingsServer_Name → General (not Settings → Plex Web → General).
See Reporting Issues with Plex Media Server for detailed information.

Reset your file permissions, even if DSM says they are OK.
You have many (hundreds) “Permission denied” errors in the log files.
Make sure the system internal user PlexMediaServer has at least read-only access to the appropriate directories / shared folders.
See FAQ 19: Setting permissions to allow Plex access to media files
Be sure to check the box next to “Apply to this folder, subfolder & files.”

Jan 04, 2022 19:00:09.755 [0x7fb999a8bb38] ERROR - Error opening file '"/volume1/STUFF/Media/Movies/Swan Song (2021)/Swan Song (2021).mkv"' - Permission denied (13)

Rescan the libraries after resetting the file permissions.