On your old iPhone, open Settings → Back Up & Restore My Data and save a backup file. Keep it outside the app, somewhere your new phone can access, such as iCloud Drive in Files. On the new phone, select that backup file to restore it.
The backup includes songs, chords, patterns, recordings, settings and tutorial progress. There is no automatic sync. Restoring replaces your current data with the selected backup, so save a separate backup first if you need to keep the current data. Pro purchases are not included in the file; use Restore Purchases for Pro access.