Actually… the local plex user on your Synology is no longer required to be an admin… which had caused problems with recent updates of the Synology platform.
You can find a summary of those changes from some time ago in this forum post:
The post also includes some instructions to fix potential issues.
If your issues still persist and you cannot download the logs via the Plex Web app, you can also access them via your Synology’s File Station app:
https://support.plex.tv/articles/200250417-plex-media-server-log-files/#toc-1
