If you opt to sign-out all connected devices while resetting your password, this includes the Plex Media Server itself as well. That means you’ll need to re-claim your server.
There’s different ways to do that, e.g. by accessing the server through its local IP address (http://[Syno IP address]:32400/web) and signing the server in (Settings > [Server Name] > General → Sign In). Another option is described in the Syno FAQ.
