Transferring music from old iPod to new iPod

I have an old iPod Nano that I've used for many years, but it's not holding it's charge any more. I now have a new iPod Nano 5th Gen, which I'm trying to transfer all my music over to. All the music has come from CDs over the years - nothing from the iTunes store, so there's nothing in my iTunes account to transfer over.

I've managed to transfer the music from the old iPod to the new iPod, but I cannot figure out how to get the music from the "iPod Music" to the "Library Music".

Help! It's taken HOURS to get to this stage so far, and now I feel like there's something I'm missing (hopefully!).

The settings are set to Manual, and there's nothing else I can find that seems like it would help.

Thanks!