Apple TV app and HomeKit

The Apple TV app on third party devices is not supported for HomeKit access, other than some of those devices being an AirPlay accessory themselves.

The Apple TV box (4th generation or later) can be a home hub for HomeKit, with some limited functionality through Control Center for some accessories. The Apple TV app is not involved in that.

Add a HomeKit accessory to the Home app (iOS, iPadOS) - Apple Support

Control HomeKit scenes and cameras - Use tvOS Control Center on Apple TV - Apple Support

You may have to do some extra homework to find out what each accessory is capable of, and how well it integrates with HomeKit controls and scenes on Apple TV. I am not aware of any list with such deep details.

For many HomeKit devices, the Home app or a device-specific app on iPhone or iPad is the interface.

Certain HomeKit devices may have a widget in Control Center on Apple TV. It depends on the accessory, though. E.g. cameras like a doorcam may allow to show the video feed there.