Home app on iPhone not showing HomePod to select as home theater audio

They need to be in the same Room . Have you assigned them to the same room?

Look in the Apple TV 4K icon in the home app and this only works with that model ATV and the big HomePods (not the Mini)

All software should be updated to the latest on the ATV, HomePod and the iOS device you set up HomePod with

• Use your iPhone, iPad, or iPod touch to assign your Apple TV and HomePod to the same room in the Home app.
• With iPhone, iPad, or iPod touch: In the Home app, press and hold Apple TV, then scroll down and tap Default Audio Output. Select the HomePod or stereo pair that you want to use for home theater audio. Tap Back, then tap Done.
• Or you can set this up in the Apple TV 4K as instructed here:

Set up home theater audio with HomePod and Apple TV 4K - Apple Support

Are they the big HomePods? Is it an Apple TV 4K? You need both those devices and you also need to update your HomePod and Apple TV to the latest software

See: Set up home theater audio with HomePod and Apple TV 4K - Apple Support to check you’ve done everything

You’re welcome

hello, the homepod pair is not showing in the default audio list even though i have added them in the same room.