There’s a feature called “One Home Screen”, it does exactly what you’re looking for, and it is tied to your iCloud. It works well for most I think, but not for me.
You turn it on in the settings under users and accounts, select the default user for the user you wanna use it with, and it’s under iCloud.
It never works for me, whenever I turn it on it goes crazy, deleting a bunch of my apps and adding apps that should no longer be on my Apple TV‘s, it is a huge headache for me.
I have tried multiple ways to fix it, but nothing ever works. Not only that, whenever I attempt to get it to work, it seriously screws up whatever Apple TV I turn it on.
That’s not to say that everyone has this issue, I have seen post square it works perfectly for others.
I wish there was a way that you can lock one particular Apple TV as the main, or have it as the key, and then copy all the other Apple TVs to that one. And then any changes after that I could turn off the lock and then they can all sing together.
Another issue I have seen with other peoples Apple TV‘s if they have a lot of apps installed, if they get a brand new one, but it has a smaller storage space than their previous Apple TV, when they go to turn on one home screen, there’s not enough space to download all the apps.