I’m not able to see ‘Apple Music’ in backup, when I select “Show all apps”

That's because the Apple Music app contents is not part of the backup.

Apple Music is either directly synced to iCloud using the iCloud Music Library feature from the Apple Music or iTunes Match subscription service, or is synced from a computer directly, which implies it already exists somewhere other than the iPhone or iPad form where it can be recovered.

Music is not backed up to iCloud.