The open WiFi thing I have yet to see any evidence of, as discussed elsewhere in this thread, and while HDMI has supported ethernet for years I legitimately have never seen a device claim to actually use it. You'd need both the TV and something it's connected to supporting it for it to become a risk.

The same wires are used for HDMI ARC, so any device supporting ARC (most TVs) inherently can't support ethernet on the same port.