Yeah I think you need one of the 3rd party backup apps to get playlists.I just used samsung smart switch. There was never an option to save playlist only save the actual song in folders on the sd card
FWIW, I started using Next SMS a while ago (maybe 8 years ago? It started as Handcent SMS on my Galaxy S3) and I've stuck with it, good text app IMO with just a few bells and whistles, but enough for me.