Plex says “unauthorized” for one of a couple reasons:
- It sat too long before claiming
- It doesn’t have an internet connection
- It thought it was claimed before and the credentials are damaged.
- The Synology and you are not on the same RFC-1918 compliant network (you are remote from it)
The best way to attempt to correct (fix the credentials)
This How-To is written in English but the menus are in the same position 
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