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My homepod mini responds "I couldn't find _______ in your Apple Music library." It doesn't matter what you fill in the blank with. This was working a couple of weeks ago. Homepod updated to 15.5, which did not fix things.
HomePod mini
I don't see this on my homepod (home screen, long press homepod, gear icon settings).
Primary User is my name (not "HomePod Account"). Siri settings are:
That is it. Those are all the options / settings available in 15.5.
Open the Home app, tap Home 
in the upper-left corner, then select Home Settings. Tap your user profile under People, and turn on:
Nope. Siri cannot find any music on my Apple Music. I have over 1000 CDs rippped Apple Lossless. I play these on my Sonos system all through the house, and via Apple Music on my Mac mini. I do have to select my library on Apple Music, not the default. And my HomePod used to work well. It just doesn’t anymore. No changes on my side.
In my experience Homepods cannot use Homesharing to find and play music from the Mac Mini (eg ripped CDs). For example You can use an Apple TV that uses its Computers app to play Homesharing (Mac Mini) music to the Homepod(s) that are default audio output for that ATV. However Homepod Siri is not very reliable for this and I sometimes get the same error message as you. I have to remember to wake up the ATV before making a request to Homepod Siri.
Unfortunately Homepods seem to be optimised for Apple's music subscription service.
Again, let's remember this is a new problem. I've had the homepod mini since it was first available. I never connected it directly to my system, just to my network. It always used to play whatever we asked, even if I did not own that music in my disk library.
Now, just this month of May, it will not play anything. "I cannot find ________ in your Apple Music Library."
There was another thread about this, and apparently it was a system outage that Apple corrected. Except I am fortunate enough to get to experience a similar problem but without a quick resolution.
I have attempted all the pedestrian solutions. I have disconnected, restarted, re-installed, re-added the homepod mini and my iphone multiple times. The result is the same. No change.
From what I can tell, the problem is not on this side of the fence.
I am having the same issue since upgrading to HomePod version 15.5, so I think it must be related to the update. I also have had my HomePods for a while and have never had this issue prior to installing the update. Will chat with Apple on Monday and submit a trouble ticket.
See if restarting it helps: Reset HomePod – Apple Support (AU)
See if closing the app and restarting your phone helps:
Close an app on your iPhone or iPod touch - Apple Support
No joy. Reset, reloaded, re-added. Still the same response.
Try Home app > long press on HomePod > Scroll down to settings > Music & Podcasts > Primary User > Sign Out. Then sign in again.
tt2
Primary User is greyed out. I cannot select it, nor sign out. Nor can I select "Reduce Bass", also greyed out.
I reset the homepod, then set it up again (again, again, ...). I can now sign out, and sign in, but nothing changes. Cannot find ______ in Apple Music.
Have you enabled recognize my voice?
tt2
Recognize my voice is on. Media is Apple Music (use in home: on, lossless audio: on, dolby atmos: on).
My homepod mini will not play music.
