Can I copy app data from an old iPhone backup to a new, set-up iPhone? I recently got a new iPhone. I backed up my old iPhone in iTunes, and then set up my new iPhone as a restore-from-backup. However, I was just looking at my new iPhone and realized some apps failed to copy over.

Is there a way to copy the app data from the old iPhone to the new-but-already-setup iPhone, or do I need to start over?

I know I can download the apps, but can I transfer the data? Part of this is game data that I know does not live in iCloud or any server.
After iOS 8, according to this document by Apple, app contents are no longer backed up by iTunes. I suggest using iMazing to backup your old phone, and restore it on your new phone to get the app content.