Are all those devices of yours in the same subnet inside your home network? It almost sounds like the clients fail to access the server locally and stream through a relay server of Plex instead. Some routers establish different subnets by themselves (e.g. for wired vs. wireless networks, 2.4 GHz WLAN vs. 5.0 GHz WLAN, guest network vs. main network…), sometimes this happens if you have other active network components like a WLAN access point which creates its own subnet.
Those relayed/indirect connections have a limited bandwidth. You can verify this via the server’s dashboard while streaming to your TV (-> you should see information if the stream is local, remote or indirect)
Plex usually requires a very basic internet connectivity – though that’s not used for the actual stream (there’s a dedicated thread in the tips & tricks section discussion what it’s used for and how to minimize it).
