MoveFiles is a basic app that moves files from one location to another.
In order to work on newer Android releases, it requires the manage external storage permission.
In order to avoid tying up resources, it runs periodically (around once per 15 minutes, unless the system is asleep).
Subdirectories are not searched or moved, only files.
Binaries can be obtained using the F-Droid client, from my custom repository: https://yasmar.net/fdroid/repo