Apple Music keeps asking me to log in using deleted account

For various boring reasons I've ended up with multiple Apple IDs. I finally managed to delete one of them, but now I get asked to log into it every hour or so by the Apple Music app. No matter whether I provide the correct password or cancel the operation, an hour later it will ask again.

As far as I'm aware it's not been used for anything, has no prior purchases, no music, movies, apps, games, subscriptions or anything else. I also asked for it to be deleted a couple of months ago, which apparently happened, so I've no idea why it keeps asking me to sign in. If I attempt to sign in with it at icloud.com, it says "You do not have an Apple ID.". If I sign in with my main Apple ID instead, it just comes back an hour later asking for the same old login.

How can I make Music stop asking for this old Apple ID?