I’ve had a super old DVD player connect to the internet over an hdmi cable to my blue ray/surround sound system device that had Ethernet connected. It used the connection to patch itself, didn’t even ask if I wanted to.

Even a $7 AmazonBasics HDMI cable has Ethernet support (https://www.amazon.com/dp/B014I8SSD0), not that this really matters since hardly any devices ever supported Ethernet over HDMI.

Also, Ethernet over HDMI is limited to 100 Mbit/s which would make it slower than most modern Wi-Fi networks (leaving aside any possible reliability issues).

The first monoprice cable that came up on Google says it supports Ethernet https://www.monoprice.com/product?p_id=42682