Hi Bront,

Currently drag/drop within the file webpart is not set up. In 12.2 we added the ability to move files around via the 'move' button on the button bar.

If you don't see the button, you can add it by clicking 'Admin' -> 'Toolbar and Grid Settings' -> and drag the 'move' button onto the button bar.

This then allows you to choose a destination folder once you have the file selected.

Thanks,
Nick