The backup was a clone of whatever was physically on the phone. There are two places music can live: physically on the phone which would have required you to download each song at some point either directly from the phone or transferred from iTunes (now called Music) from a computer. OR to keep all your music in the cloud. So two things to consider. Was the music originally transferred from a computer? If so, that music would still be on the original computer OR were you paying for Apple Music in which case the music, along with playlists, would still be in the cloud. Also, any previously purchased music will always be available to be redownloaded for the rest of your life. If the music was not download but instead, imported from CDs then that would have required a computer. Therefore you could return to the original computer and re-sync the music.