The answer is to grab a Pi or similar tiny box and treat the TV as a dumb monitor.
This works very well.
This works very well.
Edit: nevermind, I've completely misread your comment to be about Pi-hole :)
Can it also turn on/off tv? I think HDMI allows that but not sure if Pi can do that
To turn on and off a TV you need an HDMI port that supports CEC. The Pi does, so you just need to install cec-client.
As for OS, you should use the general purpose Linux distro that you are most familiar with. If in doubt, use Gunnar Wolf's Debian for Pi, which is as close as you can get to 100% Debian on a Pi.