I haven't been able to access my libraries for months

Server certificate is looking valid.
NAS device is live and has been phoning home to plex.tv ~7hrs ago. So that indicates it is alive and well.

In addition to the above by @FordGuy61, verify that your web browser is allowed to access the local network while showing the “web sites” app.plex.tv and watch.plex.tv
See Important note about the Plex Web app - Local Network Access