Unable to add my son to Home after creating an iCloud account

Also, you don't need to add a person to your Home to allow them to play music on your Home Pod. Anyone can use Siri to play music, they just won't be able to play any personalized playlists, but they can certainly use Siri to play any song, artist, or album on the HomePod.

To further pursue the issue of not being able to add your son to the Home app:

• Is the child under 13, where they are required to be a member of a Family Sharing plan?
• What happens when you attempt to add after following the steps provided by Vancouver22?

See: Share control of your home - Apple Support

• make sure your so sons device is running the latest software. he needs at least iOS 16.2
• Turn on two-factor authentication for Apple Account and iCloud for Passwords and Keychain.
• Make sure that you and the people you invite haven't blocked each other's phone number or Apple Account. Learn how to manage who you have blocked on iPhone or iPad and Mac.

• Tomorrow Apple will release OS 26 to install the latest software on all devices.

Or also see : Invite others to control accessories in your home - Apple Support

As I posted above you can Invite others to control accessories in your home so he can use the HomePod. Change the Speaker access settings to allow others on same network. He could at least airplay his device to play on HomePods. I’m not sure how asking Siri would work on his current OS. He should be able to use his locked home screen to control playback if you change these settings.

The above and below are two different things. Family sharing is also different.

If you had already upgraded the Home to the new architecture (you might have by now and it’s not the same as software updates on HomePods, it was a Home upgrade) then an iPad on iPadOS 15 will not support him using that device to use HomeKit. Invites will not go through.

Please refer to all documentation posted in blue.