Unable to locate media on Synology NAS

No. That’s not how it’s done. Also, on Linux, the delimiter is / not \. If you attempt to use \ it will never work.

Linux interprets \plexmediaserver\homes\me\Drive
as if it were plexmediaserverhomesmeDrive which is meaningless.

You must use: Control Panel - Shared Folders - Create

Remove everything you have done on the command line. You will fill up the tiny partition used by the OS if you don’t. Everything must be done as a Synology “Shared Folder” . When you create the shared folders, they will be accessible to Plex by the name /volume1/movies (or whichever names you create)

In this announcement, I showed how to edit existing media shares.
The permissions set in this announcement are the same you need to use for PMS on your new shares.