Yes, this issue is a bit maddening. I have 3 Apple TVs at 3 different locations (a total of 2 different local area networks). The Apple TV v4 seems to work fine with HomeKit, but the Apple TV v3 was showing as disabled, and after trying a few different things with it, it no longer shows up at all now!
(Yes, all logged in to the same iCloud account. Yes, 2-factor authentication enabled. Yes, key-chain enabled for iCloud. Yes, updated Apple TVs to latest firmware version. Yes, rebooted Apple TV / logged out of iCloud and logged out / rebooted / logged back in, etc. etc. rebooted in various combinations.)
Apple's software quality seems to be spotty at best and poor at worst, and the software usability is simply awful. I was only able to get the Apple TV v4 working thanks to articles written by others who encountered these inane challenges, but I haven't found anything that works (in my environment) to get the Apple TV v3 working with HomeKit.