The aging TV probably doesn’t know the root ca used by Plex‘s when creating your server’s certificate. Hence it decides to not trust the server/certificate.
As mentioned in the notice, you can try the following:
Plex TV app: Settings → Advanced → Allow Insecure Connections = Always
Plex Server: Settings → Network → Secure Connections = Preferred
You may also need to disable Strict TLS Configuration on the server Network settings page.
If none of that works, then consider acquiring a streaming box/stick - AppleTV, Roku devices, Android TV devices such as onn (Walmart), Amazon FireStick, etc.