Shazam in Control Center doesn't sync identified songs to Apple Music

I'm having the same issue, exactly as described by the OP.

Songs added by the Music Recognition Control Center widget are added to Shazam like expected, however they do not get added to the My Shazam Tracks playlist.

The playlist will update if you manually toggle the "Sync Shazams to Apple Music" setting off and then back on in the Shazam settings. Songs identified with the Shazam app update the My Shazam Tracks library as expected.

Sync Library is turned on.

The Music Recognition widget is not working correctly (iPhone 14 w/ iOS 16.3.1)

Hey RealJerzy,

In your troubleshooting did you also make sure that the Sync Library option is turned on with Apple Music? We found "If you can’t add songs to a playlist, make sure to sync your music library with Apple Music." that leads to turning on the Sync Library feature here: Use Sync Library to access your music library across your devices - Apple Support

The above details can be found under "Apple Music" here: Use Shazam with Apple Music, Snapchat, and more - Apple Support

Let us know what you find.

Take care!