How to add apple music back once deleted

You cannot add Apple Music files back into the library once they have been removed, nor transfer downloads made in one library to another. They must be downloaded from the iTunes Store directly in order to work. The only exception might be if you were looking at a scenario covered in Empty/corrupt iTunes library after upgrade/crash where reverting to an older version of your database would enable it to use the Apple Music items that were present in the restored library.

tt2

Have you looked in your recently added playlist?

I don't have any hands-on experience with Apple Music files but I know that for some purposes they do not behave like other music files. I would not exclude the possibility that you have to add them by re-downloading directly from Apple, but maybe somebody can tell me differently.