Hello 1-smonm-1,
Welcome to Apple Support Communities.
From what I understand, you have upgraded to an iPhone SE and on restoring the device via iCloud, your iTunes playlist haven't transferred over, correct? I'm here to help you take a look in to that!
If using iTunes for playlists, you would want to transfer the playlists from iTunes to your new iPhone. iCloud will storage purchase history and you are able to re-download songs you have purchased in iTunes. iTunes Match would allow you to sync iTunes playlists between devices. Here are a few article to read over on resolving this issue:
About missing information after you restore your iPhone, iPad, or iPod touch with iCloud Backup
Redownload apps, music, movies, TV shows, and books
Subscribe to iTunes Match
Hopefully this helps!
Cheers!