There are no receivers on the market that act as HDMI Ethernet network switches.

Are there any examples of TVs doing this, or is this just a hypothetical?

There are some TVs that will try to connect to the internet via non-obvious means (Samsung TVs were mentioned elsewhere in this thread). TV manufacturers aren't spy agencies though. They're not going to put in that much effort to sneak an internet connection, when most users willingly connect their TVs to WiFi anyway. If I can't find an article about a given TV sneaking in an internet connection, I would be pretty confident that it doesn't.

> They're not going to put in that much effort to sneak an internet connection,

The profit from collecting data on you and displaying ads on the TV is greater than the profit from the sale of the TV.

They absolutely will go to whatever lengths they can.

https://www.cnet.com/news/as-smart-tvs-become-the-only-optio...

https://www.theverge.com/2021/11/10/22773073/vizio-acr-adver...

I've been looking for years and I have yet to find any systems (TV, receiver, or injector) which actually take advantage of this feature.

They have been for a while. But are these actually used for IP connectivity? If that was the case, a laptop’s HDMI port should show up as network interface, which it doesn’t, at least not on my machine.