Hi and welcome to Android Central! What music app are you using? Most subscription apps like Google Play Music or Spotify allow you to download playlists from your music library screen, but you don't really have direct access to the music files. If you are using one of those apps, you will need to redownload those playlists when you are on WiFi. If they are FLAC or MP3 type files that you have downloaded directly to your phone, you could plug your phone into your PC and drag and drop those files into a folder and then plug your S7 into the PC and drag them from the computer to your new phone.
If you could let us know what app you are using we could provide you with some more app specific instructions