Why won't my Apple TV 4K work as a HomeKit Hub.

First update all Software. (iPhone, ATV)

Try to sign out of iCloud in settings- Users & Accounts - Your name - iCloud .

Restart your ATV. Once it’s restarted go back into settings and sign back into iCloud. You should then see AirPlay & HomeKit prompting you to set that up. Follow the on screen instructions. Make sure to Allow Access and be on the same wifi network. Your Apple TV should then display in the Home App and be listed under Hubs & Bridges as connected or standby.

There should also be no conflict using the same Apple ID with other hubs, in fact you should be. - so sign the old one back in. If it’s a problem using Siri on the remote to use HomeKit, try rebooting your wifi

Set up your HomePod, HomePod mini, Apple TV, or iPad as a home hub - Apple Support

If your home hub isn't working as expected

• Check that your HomePod, HomePod mini, Apple TV 4K or Apple TV HD, or iPad is up to date. 
• Make sure that the user signed in to iCloud is the primary Home app user, and not an invited user. 
• Turn on iCloud Keychain and two-factor authentication for your Apple ID.
• Check that the device that you set up as a home hub is in your home, connected to your home Wi-Fi network, and powered on.

I would encourage you to use the ATV HD & iPad as Hubs as well. They are intended to take over if another fails (standby vs connected) Unless of course it’s bothering you that you can’t use the ATV Siri remote to perform HomeKit tasks with the Siri button but you can still ask Siri on your iPhone or on your Mac (if it has Siri). It’s not just Hubs that can perform the tasks. Any Apple device signed into the same Apple ID you’re using for your Hubs can, Apple Watch will as well. Having said that, keep all your devices signed into the same Apple ID. & connected to the same home wifi network (*some do experience better results having Apple TV connected to wifi) so you have continuous syncing.

• If it is the Siri remote (you didn’t really say what the error was) it might be the remote that needs troubleshooting: If your Apple TV remote isn't working - Apple Support
• As to your dead Homepod, if a full Reset (pressing the top method) didn’t fix it, make sure to remove it from the Home App if it’s still there and get it signed out if your Apple ID - you can check on this in iPhone settings- Your name- scroll through the device list and Remove it. If it’s still under warranty you can get in touch with Apple to have it replaced.

Do you have any other Apple Hubs like a HomePod for example? if you do, reset the HomePods. Sometimes you have to delete Home in the home app and set everything up,again, which of course is a pain. Resetting Apple TV is another option but this restores it to factory conditions. Otherwise it could be a wifi issue.

When you signed out on your other Apple devices make sure keychain got turned back on, on all devices. I signed out on an iPad once and HomeKit wasn’t working after signing back in , then I noticed keychain got turned off on the Mac.

I developed some issues with my lights, I use the Hue app made for the lights instead now. Some of the accompanying Apps offer advanced settings , one being to enable HomeKit & Siri.

Ok , if you can use your other Apple ID on the old 3rd Gen ATV, try testing that so it’s not interfering as a malfunctioning Hub