how to migrate the music app to my new mac

When you capitalize the word Music, then we understand that to mean the application. On the other hand, if you mean your Music folder, then add the word "folder" so we will understand the reference. The easiest solution is to copy the /Home/Music/ folder on the old computer to an external USB drive large enough to hold the entire folder. Then move the drive from the old computer to the new one. Locate the /Home/Music/ folder on the new computer. Select and copy the content of the folder on the external drive to the /Home/Music/ folder on the new computer. Note that you cannot replace the Music folder on the new computer with the Music folder on the external drive because macOS will not let you. But there is no issue with transferring the content of the old Music folder into the new Music folder.

To avoid permissions problems, it would be a good idea to have an account with the same user_name on the new computer as used on the old one. If they are not the same, then you will have to change the user_name on the new computer to match the one on the old computer: see Change the name of your macOS user account and home folder - Apple Support.

You cannot use the Music/iTunes application from your old computer on the new computer. The new computer already includes Music (which has replaced iTunes in Catalina) as part of macOS.

I suspect you may have meant something else, so please post a clear explanation of what you need to do.