This is impacting a new Macbook I bought and I cannot play previous purchases under my appleid. Additionally, there a "deauthorize all" button does not appear. This new macbook does show up under my devices using my ipad to view it.
[Re-Titled by Moderator]
MacBook Air 15″, macOS 14.3
I had the exact same problem. I could not authorize my new Mac via the Apple Music or Apple TV apps no matter what I did. I would only see 1 authorized in Account Settings but it would still tell me there were 5 if I tried to authorize my new one. Finally I tried using the Books app instead. From there I went to Account -> View My Account -> View Account Settings and clicked a second View Account Settings from the pop-up menu. Then a pop-up dialog will appear telling you it will take you to the App Store. Click OK. Finally I saw the "Deauthorize All" button that was not showing up in the Account Settings on the other apps. I clicked it and it told me I cannot deauthorize all computers more than once per year. But it was a false positive error message because I was able to authorize my computer from Apple Music after that. Phew! What a convoluted process. Hope my workaround helps you as well!
How to deauthorize Apple Music from other devices
