The log files are from Plex Media Server running on a Windows 10 system, not on a Synology NAS.
Might you have two installations of Plex Media Server, one on the Synology and one on your PC?
Look in Settings → Authorized Devices. How many servers are listed?
To retrieve the correct logs, make sure you have the correct server selected on the left hand side in Settings.
You can also manually retrieve the log files from the Synology NAS.
See FAQ #13 in Synology FAQ - Questions, Answers, and a few How-To’s
