Hi DannyDove,
Thanks for coming to Apple Support Communities for help getting your music synced on your new iPhone SE.
Synced music is not part of an iTunes or iCloud backup. If you were previously syncing the 5c with the MacBook Air and using music there, that should be able to sync with your new SE. What you may be seeing on the SE are purchases from the iTunes Store that can be downloaded again: Redownload apps, music, movies, TV shows, and books. These purchases may not be in your MacBook Air iTunes library.
As long as you haven't synced your new SE to any other iTunes library since you received it, it doesn't sound like you are in danger of losing any music that is on the iPhone or MacBook Air. You should consider keeping an iTunes library backup if you don't have one already: Back up your Mac with Time Machine.
You can even set up iTunes to check for available downloads which will download anything that you purchase on your iPhone: Download previous iTunes purchases on Mac
"Set iTunes to check for purchases automatically
- In the iTunes app on your Mac, choose iTunes > Preferences, then click Downloads.
- Select “Always check for available downloads.”
Here are syncing instructions: Use iTunes to sync your iPhone, iPad, or iPod with your computer.
Have a great weekend!
