Server Version#:1.42.1.10060
Player Version#:Various &plexamp
Simple Issue: Changing your plex password DOES NOT change plex user access in DSM.
I had this issue and saw all sorts of complex (SSH/delete/reinstall/change this and that) that just seemed unnecessary.
I west to DSM/Control Panel/ Users and double clicked PLEX. Under the info tab I saw the Plex user PW had not been changed in ages. Updated the PW with my new plex PW and clicked save. Exited DSM.
Restarted all my plex apps and they worked just fine.
As far as your local server security is concerned, you have destroyed it.
Changing the Plex password on the NAS has removed the super secure, unknown by anyone, not even Plex themselves, secure password which is installed by the Plex installer package.
A hacker may now gain access to your Plex server very easily, so I would advise you to uninstall Plex, delete the Plex user currently on your NAS and then reinstall Plex. Do NOT touch the Plex user account on your NAS again.
Since you did not change your Plex account password, if your account was compromised, then you have done nothing to address that.
Open Plex/Web > Settings > Account and change the password there and be prepared to do all the things (SSH/delete/reinstall/change this and that) you thought you could avoid.