Accessing Apple Music on MacBook with different Icloud account.

I have two apple IDs. One for work and a personal one. My macbook was set up with my work email, but I use apple music with my personal email.

Other threads have mentioned that I can sign into my apple music on this macbook if I go to System Settings > AppleID > Media & Purchases > Click Manage on Account and enter my apple id associated with my music account. This does prompt a sign on screen in apple music, however when I enter the details of my appleid associated with apple music. It accepts it, then does a loading screen saying "Accessing Music Library", then goes back to the sign in prompt with my work appleid.

Is there any step I'm missing? Or any other way to get this to work. I know it's not a password issue as I was able to access the apple music web browser with the same password I'm using to sign in.