There is no guarantee that the backup folder is in the same place on a different phone. Your new phone is most likely looking in a different location to the old phone.
This article mentions this fact.
This article gives a full description of how SD storage work.
You can test this by creating a new uniquely named folder in your backup folder using your old phone and then trying to find that folder in your new phone. Another test would be to see if you can remove your SD card from your old phone yet still see your backup files on it.
The backup files will be visible when you navigate to the correct folder. If no backup files are displayed then it means you do not have any backup files in the folder you are currently viewing.
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