I gave up after a few hours of signing out if this and rebooting that, and ensuring all the ducks are in a row. For giggles, today, (the next day) I looked at Settings>Accounts>iCloud on my TV, and low and behold, HomeKit is showing and connected. I then set up Home on the phone and turned off WIFI to simulate being away from home, and everything is now working as intended both on the Phillips Hue end and the Apple Home application.
I must say, there's definitely room for improvement, both on the accessory maker side as well as setting up Home on the iOS side.
On the Phillips Hue side, I opened the package when it arrived, it contained two white 800 lumen bulbs along with the Phillips Bridge, and a piece of paper that basically said, plug it in to power and my router/modem, download the app, and follow the instructions. I did, but when I went to pair the bridge to my phone, it said it couldn't, and didn't say why. After fiddling a bit, the app told me there was an "update" to the app, so I applied the update hoping that would fix the issue. It didn't. After a bit more fiddling, the updated app informed me that there's a newer app, and that this app will still work, but isn't being updated anymore. It kindly offered to download that app, which I did. Then, when I ran the second app, it paired right away. Then... it informed me that there's an update for this app. So.. feeling daring, I decided to update this app hoping it wouldn't break anything, and, luckily, it didn't. At that point, everything was working fine between the Phillips App and the bulbs/bridge, but I wanted to be able to set up my TV as a hub, and have the ability to control my lights from Borneo, and do cool stuff like turn on the lights when I pull in the drive....
... so to the Apple Side. Two Factor on, check. Signed into iCloud on all devices under the sun, check. iCloud keychain on, check. All devices signed into the same WIFI network, check. Signed out of and back into and toggled every imaginable switch with various reboots, check. After a few hours of that and searching the web for answers, I finally gave up. Checked in on it the next day, and finally the Apple TV had connected to HomeKit on it's own during the night or sometime the next day.
If there's one word of advice I'd give, it's to simply sign out of everything, reboot everything, sign into everything, ensure two factor and iCloud Keychain are enabled, and then wait... like 24 hours, and see where you stand at that point. Apparently, enabling HomeKit on the TV falls pretty low on the iCloud server's totem poll, so sometimes it just takes some time for some of these network aware devices to actually become.. well, aware.
Finally though, now that everything is working, I'm excited that I can turn two light bulbs on and off from anywhere, and look forward to getting more smart home devices up and running such as door locks and thermostats and the like, plus whatever stuff comes down the pike that hasn't been thought of yet. We do have to take into consideration that we're still in the baby steps era of the "Internet of Things", and over time, things will certainly get smoother than they are now. I go back to a time where you had to manually dial a phone number to connect to the internet or a BBS, and you had to know a bunch of codes to put your modem in the right mood to talk to whatever you were connecting to, but now, you plug in a computer to power and a router and everything just works, and is considered a given.