Connecting HomePod mini to my MacBook Pro

You need an iPhone, iPad, or iPod touch to set up a HomePod. From HomePod mini - Technical Specifications - Apple:

System Requirements

• iPhone SE, iPhone 6s or later, or iPod touch (7th generation) with the latest version of iOS; or iPad Pro, iPad (5th generation) or later, iPad Air 2 or later, or iPad mini 4 or later with the latest version of iPadOS
• 802.11n Wi‑Fi internet access

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Do mean that your Mac has macOS 11.6 Big Sur? If so then it should be compatible with HomePod. This should be the relevant section of the article above:

Stream audio from your Mac

1. Make sure your Mac and speaker are on the same Wi-Fi or Ethernet network.
2. Open Apple Music on your Mac.
3. To the right of the volume slider in Apple Music, click AirPlay .
4. Click each speaker or TV that you want to play the current audio on.

If you can't see the AirPlay icon  or if you want to stream audio from a different app:

1. On your Mac, select Control Centre  in the menu bar. 
2. Click AirPlay  under Sound. 
3. Select a speaker you want to play the current audio on.

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You should be able to see your HomePod like this on macOS 11.6 Big Sur:

After which all audio output from your Mac should go to your HomePod, albeit with a slight delay. Is the HomePod set up to allow playback from Everyone, or Everyone on the same network? Could there be some firewall issue blocking connections?

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What version of macOS is your Mac running? You should see the HomePod appear in the volume control settings in the task bar and in iTunes/Music etc. If your Mac has the Home app the HomePod should also appear there.

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In the Home app on your Mac right-click on the HomePod mini and click Settings... You should be able to rename it from there. It would appear to be called 177 Plymouth in your screenshot.

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See Use AirPlay to stream audio - Apple Support. As long as the HomePod and MBP are on the same wireless network you should be able to AirPlay content from the Mac.

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You're welcome. 🙂

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