Emby does local auth I believe, but since Emby is run by a company just like Plex who knows if it will stay that way long term. Probably would be best to change to the server not connected to any corporate entity (Jellyfin).
It’s been this way on Plex for like +5 years now.
If these are smart TV clients you’re referring to, the reason they don’t work when Plex is down is because the actual client does not exist on the TV set. It’s just a small launcher that downloads the client from the Internet when you start it. I’m not sure of the reason for this (likely has to do with how little storage space most smart TVs have), but the best way to avoid it is to use a client on a streaming device.
