Smart tv tracking

I have an LG Smart TV connected through my VPN router, which uses DNS-based ad and tracker blocking. When I inspect the DNS logs on my router, I see that it constantly blocks LG tracking and advertising domains. I lose some functionality by doing this, but I think it’s worth it.

Is ad- and tracker-blocking DNS sufficient? I’m considering disconnecting the TV from the internet and using an HDMI connection to my Linux PC instead. Could connecting the TV to my PC via HDMI allow the TV to spy on my PC or access the internet through the HDMI connection?