Plex Server was clearly running as I was able to connect via http://<My Synology>:32400/web/index.html

But it was not responding to any request to display Libraries or to play any Movies… To solve this, I had to :

1. Stop the package Plex via the DSM Package Center
2. Log in my NAS as an administrator, in a SSH console, via Putty and enter root mode.
3. Find Plex process still running via the command: ps -gaceux | grep plex
   1. This command displayed: plex 13150 0.2 0.2 677640 17832 ? Sl Dec17 7:41 Plex Media Server
4. Kill plex’s remaining process: kill -9 13150
5. Possibly do also delete the Plex’s Plugin Service as done here.
6. Start the package Plex via the DSM Package Center

Et voilà.

IMO, the problem was that I didn’t stop properly Plex Package before updating my DSM. The Plex instance running at that time apparently didn’t completely shutdown. But it was not really running fine anymore either. Unfortunately, that instance was preventing a new one to start (as it was still using the port 32400).