I don't have an iPhone but my daughter does.
For music I don't sync anything to her phone. I run a navidrome server and set up an account so she can stream whatever she wants whenever. I think she uses isub as her streaming app. It does allow you to download and cache files from the server to play if you are offline
As for sms, I don't know of any way to sync in Linux, but if you use Windows, the phone link app works, as several of my coworkers have set it up. I know it installs some piece of software on the iPhone you want to sync to, maybe you could do that and try running the phone link program with wine?
I also know kde connect has a link for iOS. It's not perfect but it will do the sms linking thing.