Hello @Tiffany3323026678db
Presets only sync from one phone to the other phone for subscribed account. Using the free app, nothing syncs through Lightroom's cloud storage.
Is it possible for you to make a device backup of your iPhone 12, and restore that backup onto your iPhone 15? That is the only way to transfer presets using the free app.
Otherwise, if a 7-day free trial is available to you perhaps you can sync and then cancel before the trial ends to avoid costs. Just be sure you are signed in with the same exact email address or social app service on both devices.