I do not have access to this Apple TV and I have no way of finding out if me changing my password has worked.
If I turn off home sharing and then enable it again, will it log me out of all of my devices/anything linked to my Apple ID???
Change the password to something the ex will not be able to guess.
At that point they will either have to stop using it or sign up for their own Apple ID to use the device.
Home Sharing is irrelevant unless they are on the same local network.
Retrieving data ...