Hello Notmum,
To help resolve your issue, make sure you transferred the music as shown in this article:
Import music from a computer to Music on Mac
Import music from a computer to Music on Mac
If you have songs or music video files on your computer, you can import them into Music so they appear in your music library.
1. In the Music app 
on your Mac, choose File > Add To Library or File > Import.
2. If you selected “Copy files to Music Media folder when adding to library” in Files settings, you see File > Import.
Locate a file or folder, then click Open.
If you add a folder, all the files it contains are added to your library.
Tip: You can also drag a file or folder from the Finder to the Music window to import it.
By default, Music places a copy of each audio file in the Music folder (Home/Music/Music) and leaves the original file in the current location. For information about adding an alias to the file (instead of creating a copy), see Change where your music files are stored.
When you import an item by dragging it to the Music window or choosing File > Add To Library or File > Import, a reference (or “pointer”) to the item—not the item itself—is placed in the Music folder. You might not be able to play the song if you move it.
If you still need help. Tell us what happens when you try to play the songs you transferred to the new Mac. Please provide any error messages you receive. Also, do you have an Apple Music subscription?
These details can help the community gain a better understanding of your issue.
Best Regards.
