No, none of those plugins support attachment post type.

I have tried using the wordpress search widget and added this function to search attachments but attachments are still not searched or displayed:

function my_attachments_search( $query ) {
 if ( !is_search() ) 
    return $query;      
 
  $post_types = $query->get( 'post_type' );
  if ( ! $post_types || 'post' == $post_types )
    $post_types = array( 'page','post', 'attachment','mpp-gallery' );
 
  if ( is_array( $post_types ) ) 
    $post_types[] = 'attachment';
 
  $query->set( 'post_type', $post_types );
  return $query;
}
add_filter( 'pre_get_posts', 'my_attachments_search' );

This function worked with default wordpress search widget:

function attachment_search( $query ) {
    if ( $query->is_search ) {
       $query->set( 'post_type', array( 'post', 'attachment','mpp-gallery' ) );
       $query->set( 'post_status', array( 'publish', 'inherit' ) );
    }
 
   return $query;
}

add_filter( 'pre_get_posts', 'attachment_search' );

Gallery items are now displayed in search results. However, how can I get this to work with the default Mediapress search?

mpp_directory_gallery_search_form();

I also found this plugin which has search capability for ‘attachment’ post types

https://wordpress.org/plugins/search-everything/