I had to change my Apple ID for security concerns, resulting in my HomePod Mini stating, "This accessory is not responding." What can I do?

See Use private Wi-Fi addresses on iPhone, iPad, iPod touch, and Apple Watch - Apple Support and turn off private address for your own Wi-Fi network. Then try this reset procedure once more:

Reset HomePod or HomePod mini

1. Unplug HomePod or unplug the power adapter for HomePod mini. Wait 10 seconds, then plug HomePod back in.
2. Wait 10 seconds, then touch your finger on 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.

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Did you follow the process in Change your Apple ID - Apple Support, or simply start using a new Apple ID?

See Reset HomePod or HomePod mini - Apple Support. You will likely need to reset any HomeKit accessories, rebuilding your Apple Home under your new ID.

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