Data transfer from phone to phone did not populate non-shared photo albums

Data transfer does not in itself restore backups, it just copies system and application data, and photos are not part of that data. If you leave it connected after that is done it will initiate a restore from backup. If you didn’t wait you can still restore a backup, which will contain your photos unless you had previously synced them to iCloud. So 2 conditions:

1. If you had synced your photos to iCloud on the old phone just enable Photos in Settings/{your name}/iCloud on the new phone.
2. If you had not synced to iCloud on the old phone restore the backup of the old phone—>Restore your iPhone, iPad, or iPod touch from a backup - Apple Support