First of all, you can't add/remove/edit Home screen channels in Google TV. Any kind of customization has been removed.
Second, the whole "For you" vs "Home" thing depends on region. If your country is mentioned here , you'll get at least 5 of the usual 6 tabs ("For You", "Movies", "Shows", "Apps" & "Library). If it's not, you'll get 3 tabs ("Home", "Apps" & "Library").
Third, you get the "Home" tab instead of "For you", not the other way around.
The "real" Google TV UI/launcher is called launcherx (Chromecast with Google TV, newer 2021+ Sony's, etc. that are actually branded as Google TV).
I think the skinned version of Android TV that looks like Google TV (probably your Sony TV, especially if it's from 2020 or older) has some other launcher, not launcherx. Maybe tvlauncher or something.