I am very frustrated with my HomePod Minis random performance

If HomePod isn’t responding, first try to restart it with the Home app, you'll need to ungroup the stereo pair before you can restart each one,. Then stereo pair again

If you had used the music App on your Apple TV force quit that - if your model has a Siri remote:

• Swipe up on the Touch surface of the Siri Remote to force the highlighted app (the app in the center of the screen) to quit.

https://support.apple.com/en-ca/guide/tv/atvbbcec4f4e/tvos

In fact close all the apps you had open

Then Restart Apple TV

You can’t get to that setting when there’s no response

• Remember to ungroup the stereo pair before you can reset each one

You will need to do this:

Press the top of HomePod to reset it

If you can’t remove HomePod from the Home app, you can press the top of HomePod to reset it to its factory settings.

Here’s how:

1. Unplug HomePod or unplug the power adapter for HomePod mini, wait 10 seconds, then plug it back in.
2. Wait 5 seconds, then touch your finger to the top of HomePod and hold it there.
3. The white spinning light will turn red. Keep your finger down. 
4. Siri will say that your HomePod is about to reset. When you hear three beeps, you can lift your finger.

If you still see HomePod in the Home app after you reset it, then you'll need to manually remove it from the Home app.

Reset HomePod - Apple Support

Then set it/them up again

Share your experiences with Apple via Feedback - HomePod - Apple.

tt2

Are both HomePods on the same wifi network? Both HomePods and Apple .TV running the latest software? 14.3

Update HomePod

Use Apple TV to play audio throughout your home - Apple Support

You’re welcome.