I seem to have misunderstood the point to their comment. They’re lending support to the idea that you should unplug it from the internet whereas I initially thought they were saying that even if “unplugged” from the internet, OP’s current setup wouldn’t save their privacy anyway because the TV will send those screenshots to the internet whether it’s by via the TV’s own apps, or “through” the HDMI cable which in my mind implied either getting internet connectivity through that cable or at least sending the images to the laptop and having that send them. I couldn’t see how that was supposed to work.

I realise now that’s not their point at all, they’re saying that if it’s allowed to remain connected to the internet, simply abstaining from using the TV’s own apps and using persistently a connected device via HDMI instead, it’ll still send screenshots of that HDMI output through its own internet connection and so yes, indeed OP should disconnect the TV from the internet.