I have the same problem. After clicking on export to file, an overlay with the message “Done creating an empty archive.” appears and nothing happens.
there is no error.log in the directory wp-content/plugins/all-in-one-wp-migration/storage
just an index.php (content: <?php // silence is golden) and a status.php (content: {“message”:”Done creating an empty archive.”,”total”:0,”processed”:0,”type”:”info”})
and a folder was created with some kind of random name