Missing playlists
We upgraded a phone and many playlists are missing on the phone. We back up manually to our iMac, use Apple Music. We can see the playlists on the iMac iTunes Library.
iPhone 13 Pro Max
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If you subscribe to Apple Music, you might be able to fix your issue by turning Sync Library off for all of your devices, then turning it back on again. Learn how.
Otherwise you might try syncing the iPhone with your iMac:
Sync your iPhone, iPad, or iPod using your computer - Apple Support