I had exactly the same issue at the beginning of this month, it is due to a recent change by Plex having to do with security protocols of older TVs. It is actually very easy to fix as already reported in some other posts:
In plex on the desktop, in Settings > Network, make sure ‘Secure connections’ is set to ‘preferred’ and not ‘required’ and enter the IP addresses of your TVs in ‘List of IP addresses and networks that are allowed without auth’.
In Plex on the TV, you want to make sure that in Preferences > System, ‘Use secure connections’ is off.
You also need to enter your PMS IP address (your desktop PC or whatever you’re using) in Plex Media Servers (see the manual if you’re not sure how to do that).
Then of course you should not select ‘sign in to your plex account’ since you will not be connected to that account anymore, but instead just connected locally to your server (so that is also the potential - makes no difference for the way I use Plex - downside).
