What exactly did you do?
Have you deleted the server from here? https://app.plex.tv/desktop/#!/settings/devices/pms
If you did, you need either physical access to the computer or at least a network “tunnel” connection to it, to be able to work as if you were locally there.
https://support.plex.tv/articles/204281528-why-am-i-locked-out-of-server-settings-and-how-do-i-get-in/
I cannot provide you specific instructions for Synology.
But I assume that you can get access to the plex data folder somehow, which houses the Preferences.xml file.
Starting and stopping the Plex server should also be possible outside of the plex web app.
If your NAS is still running DSM 5 or 6, see: Synology FAQ - Questions, Answers, and a few How-To's - #31 by ChuckPa
