Use HDMI ARC or eARC with your Apple TV 4K
With HDMI ARC or eARC turned on, your Apple TV 4K (2nd generation and later) can receive high-quality audio from a supported TV, then play that audio through your HomePod or HomePod mini speakers.
What you need
Apple TV 4K (2nd generation or later)
HomePod or HomePod mini speakers
A TV that supports HDMI ARC or eARC
Turn on HDMI ARC or eARC
Go the Home screen on Apple TV and select Settings > Video and Audio > Audio Output.
Under Default Audio Output, make sure that the room with HomePod or HomePod mini is selected.
Under Audio Return Channel, select Play Television Audio. You'll know ARC or eARC is turned on when it says On (ARC) or On (eARC).
If HDMI ARC or eARC isn't working as expected
If you can't set up HomePod or HomePod mini as the default speaker for Apple TV, make sure that your HomePod or HomePod mini and Apple TV are added to the same room in the Home app. Then try to set up your HomePod or HomePod mini as the default speaker for your Apple TV again.
Make sure that your TV supports ARC or eARC. You can check by seeing if there's an ARC label next to your HDMI port, or you can contact your TV manufacturer.
You might have to turn on ARC, eARC, or HDMI-CEC in the settings of your TV. Check with your TV manufacturer for details.
Unplug the HDMI cables from your TV and Apple TV. Then plug the cables in again and try to use ARC or eARC.