music back up

An "Apple" backup does not back up your music. It has never done so.

Originally, your music would have been in your iTunes Library and what was on the iPod was a copy. Even then, an iTunes backup did not back up the music. Instead, you would do that yourself, outside of iTunes.

Regarding the music, now that many people bypass iTunes and simply buy music from the iTunes Store directly on the iPod, backing up that music appears to be more of a chore, since that music is not on your computer and especially if you have Mac OS Catalina or Big Sur, which means you cannot install iTunes.

I'm not a Mac user, but I do know that managing an iPod with those operating systems is now done with Finder. The article you came from mentions Finder, but again, that does not back up your music. Presumably though, there is a method for downloading your iTunes Store purchases onto your Macbook, which would then provide you with a first backup. Wise users never rely upon just their computer as a backup, but instead back that up to an external storage device or the cloud.

So, check in the iTunes Store to see how you download your purchases to your Macbook, there must be a way.

If you need any further information, try posting into the Macbook forum, where there may be more people who know about these things.