HomePod Siri: "Sorry there is a problem with Apple Music"

I have stereo Original Hompods as default audio output for an Apple TV 4K. A few tvOSs ago Siri music requests via the Homepods started misbehaving. It would respond to me but my partner got a response “Sorry there is a problem with Apple Music”. Online discussions over several years have reported a similar issue with no clear solution.
I tried changing the Homepod user settings in the Home app without success (other than the error started to occur for me!).

Eventually I went to Apple TV settings for Users & Accounts. My setting for “Recognise my voice” was turned off (despite Siri responding to me). My partner’s name was listed and “recognise my voice” was turned on but grayed out (She had made this setting in the Home app on her iOS device - under Home Settings).
Anyway I turned on “Recognise my voice” for myself. Suddenly Homepod Siri also started accepting her requests. Let’s see if it lasts!

So… it seems that the Primary User must have “Recognise my voice” turned on for the Apple TV in order for other (listed) users to be recognised.