iTunes library on NAS doesn't show up in iTunes

Because preferences has nothing to do with telling iTunes where a library is located. 🙂

A "library" is everything in the iTunes folder, including the critical iTunes Library.itl file. If you have everything on the NAS then start iTunes while holding down the option key and guide it to that file. If you do not have everything on the external drive then the solution will be a LOT more complicated.

A word of warning. NAS are a wonderful idea for storing an iTunes library. The problem is iTunes and NAS do not play well together, Make sure you always have a backup because your next visit here will be to ask about why your files are suddenly all jumbled up. None of us will be able to tell you why, you'll just be another one of those "NAS messes up with iTunes" posts.

There are a few other media player applications. Better? I don't know. If subscribe to Apple Music or Match, or you own an Apple mobile device, or you buy things from the iTunes Store then you have to use iTunes. There are other applications but they cost money and they may have fundamentally different ways of working. iTunes being free makes it hard to compete with.

Better would be to use a standard hard drive and use the NAS for backup. No networking though.