How to sign back into my old Apple Music account in new iPhone

My phone broke and everything on my phone was wiped. I got a new iphone 14 pro same as my old and I want to sign back into my apple music account. I have a shared account with my whole family. The sign in is not the same apple ID as the one I have. I went to the account settings in apple music to change the apple id and password and it goes to a different page and i type everything in correctly and it says im in the other apple id but it is not signing me into apple music.

[Re-Titled by Moderator]