What settings app are you talking about on the HomePod?! It has no interface. And on the Apple TV profiles must be installed via Xcode and another Apple Utility that no average users know how to navigate.
You can toggle Public BETA in the Settings app on tvOS, and on the HomePod mini and new full-size HomePod you can enable it directly in the Home app under Software Update.
If you want to run Developer BETA you don't need to utilise Xcode or Apple Utility on either. You can install developer profiles directly to any HomePod model via iOS. And to add it to tvOS you can feed it using a hidden menu by pressing the play/pause button while you are sittong on Settings, General, Privacy, Send Apple TV Analystics.