HDMI cable connection attack vectors

Is there such a thing? Nowadays the HDMI cables come with “Ethernet support” (whatever that means). Let’s say I connect my @novacustom NV41 to a smart television via an HDMI (version 2.1) cable. Does the TV have access to my dom0 computing environment? (apart from the obvious mirroring of the laptop’s screen display)

And quote from here: