Hey Lerchy,
Thank you for using Apple Support Communities!
We hear that you're having issues with your Home App asking for your Apple ID for Apple Music. We'd like to help.
Let's try a few things first:
Check that your iPhone, iPad, or iPod touch is updated to the latest version of iOS
On the iOS device that you use to set up HomePod, make sure that you signed in to iCloud with your Apple ID and turned on iCloud Keychain
You also need to have two-factor authentication set up for your Apple ID
You might also try signing out of your Apple ID and back in on the iOS device you set it up with
Go to Settings > [your name] > View Apple ID - sign out, then sign back in
Let us know if this helps.
Cheers!