Can you play your own music from iTunes?

See also

Use HomePod with Music on Mac

https://support.apple.com/en-au/guide/music/musb58944d8f/mac

The key point is to look for the Airplay icon

This is for Catalina/Big Sur. Note that similar instructions apply to iTunes in Mojave and earlier macOS.

This probably won't work if you have an AppleTV 4K with its default audio output as the Homepod(s) as it effectively blocks other devices Airplaying directly to the Homepod (but you can Airplay to the ATV in this case).

Yes. See What happened to iTunes? - Apple Support for details of the replacement apps for iTunes in Catalina and Big Sur. Music can be used to play your music and playlists.

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See Use AirPlay to stream audio - Apple Support.

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Yes.

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How can I play audio from my iPhone to play on HomePod mini?