Unable to authorize my computer for Apple Music

Hi. I had since few days issues to access my Apple Music Library from my Windows computer (see my library but can only play songs purchased with my account). I have decided to deauthorize my computer and reauthorize it again. In Apple Music, I connected to my account and clicked on Deauthorize Machine and then clicked on Authorize Machine (I am in my account, remember).

I got the pop-up window on the screen asking me to sign in my Apple Account. When entering my password, I receive the following message : Your password has changed. Please sing out from the Account menu and sign in again. This is already strange as I an already connect, but OK, I signed out and signed in again using my password; no issue. But when trying to authorize my computer, I have receive the same message again (password has changed...). I checked and I have zero computer authorized. Is there something I'm doing wrong or is the workflow not working?

[Re-Titled by Moderator]

Original Title: Authorize computer - Account login issue