Backing up my music from an older phone

While we won’t be able to directly transfer the music from the iPhone 6 to your computer to your new phone, we can use Apple Music or iTunes Match to allow you to transfer from the iPhone 6 to iCloud and then to your pc and new phone.

iTunes Match is the cheaper of the two on the month to month cost but it does require you to pay for a year. Once you have enabled the service, on your iPhone 6 you will want to go into settings>music and enable iCloud music library. Be sure to keep the music on the iPhone 6 and have it merge the music with iCloud. Then do the same with your new phone. Depending on the amount of music this could take awhile but you will see them start to trickle over. Now to get it on your pc with iTunes. You will want to go into iTunes preferences which is under the edit menu. On the general tab there will be an option to enable iCloud music.

https://support.apple.com/en-us/HT204926

iTunes March; https://support.apple.com/en-us/HT204146

Apple Music; https://support.apple.com/en-us/HT204930

As noted media is not included in device backups. All your content should be kept in an iTunes library that you keep backed up ready to restore or transfer to a new computer when needed. See Recover your iTunes library from your iPod or iOS device (or other resources). If you've allowed media to be removed from a device then it isn't possible to retrieve it from that device. Unless you pay for iTunes Match or Apple Music you should only expect to find your unhidden past purchases stored in iTunes in the Cloud.

tt2

I don't think you can upload unmatched tracks from an iPhone. See this caveat from Turn on iCloud Music Library with Apple Music - Apple Support:

When you choose Merge, songs on your device that are in the Apple Music catalog become instantly available to access on your other devices. On iPhone, iPad, and iPod touch, songs that we can't match are shown on your other devices. But you won't be able to play them on your other devices until you sign in to iCloud Music Library in iTunes.

tt2

Songs are not part of a backup. you sync through/via computer iTunes.