Connecting HomePod mini to my MacBook Pro

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.

tt2

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

tt2

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.

tt2

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?

tt2

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.

tt2

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.

tt2

You're welcome. 🙂

tt2