Hello , So its not something urgent but it was always like that since I got Cortana , it does not support music recognition nor show its icon on its main screen .
It also seem that I suppose to have a music searches folder which I don't on the list.
I have the same problem. When I ask Cortana to recognize music she says that she cannot get to the Internet. I think this feature may be unavailable in some countries and it doesn't matter if you set your device's region to US.
When the song is playing, try opening cortana and ask her "what's playing" it works fine. I also don't have the music icon. So until the final build arrives this is the only workaround.