Additional file entity fields in widget_form I've added additional fields to my file entity types and would like to have them in upload widget, just like file description.

How can I add my custom fields element using field_widget_form_alter? (if that's the way to go)
You have to add it to the field type, not entity type.  Extend FileItem and override propertyDefinitions() to add it to the field properties. Like the description you've mentioned was added by FileItem extending EntityReferenceItem:

  /**
   * {@inheritdoc}
   */
  public static function propertyDefinitions(FieldStorageDefinitionInterface $field_definition) {
    $properties = parent::propertyDefinitions($field_definition);

    $properties['display'] = DataDefinition::create('boolean')
      -&gt;setLabel(t('Display'))
      -&gt;setDescription(t('Flag to control whether this file should be displayed when viewing content'));

    $properties['description'] = DataDefinition::create('string')
      -&gt;setLabel(t('Description'));

    return $properties;
  }