It keeps syncing but nothing happens.
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See this Apple article: If you see No Service or Searching on your iPhone or iPad
If you see No Service or Searching on your iPhone or iPad - Apple Support
I accidentally deleted my music app.
Try this: Use App Library to search Music app, see this Apple article:
Organize the Home Screen and App Library on your iPhone
Organize the Home Screen and App Library on your iPhone - Apple Support
If you have find the app, tap & hold on the app, then drag to the Home screen & drop it.