Elementor Custom Control: How to get input value?

The issue here is not about getting the value — $settings['download_file'] (in PHP) would give you that value, if any.

What you’re really looking for, is to make Elementor aware of the file input changes, so that the new value will be saved by Elementor.

And the trick is, trigger the input event on the file input after the file has been successfully uploaded:

  1. In file-upload.js, find this:

    $('input[name=eae-file-link]').val(resp.data.url);
    
  2. And change it to:

    $('input[name=eae-file-link]').val(resp.data.url).trigger('input');
    

Reference.