Enabling updates for self-hosted WordPress themes and updates

I recently experimented with changing my themes and plugins to support self-hosted updates. For plugins this was relatively straight-forward once I'd found two articles, one by Misha Rudrastyh, which got me to adjust the contents of the zip files down one level (which allows WordPress to understand that the new zip file being uploaded is a replacement/update for a plugin that is already installed) and gave the basics of the self-hosted update process¹, including hosting a file that describes the update along side the zip file that is the actual update. The second article by Paul Biron showed what the current version of WordPress is expecting in the php code for plugins

However those articles don't talk about themes that much. To be fair the process for themes is very similar². However the expection of the WordPress code is different to that for plugins, so as a record here's my code:

function ningxia_check_for_update( $slug ) {
 $info = ningxia_get_remote_update_info( $slug );
 if ( false == $info ) {
  return false;
 }
 if ( version_compare( '@@@VERSION@@@', $info['version'], ' $slug,
    'new_version'   => $info['version'],
    'url'           => $info['homepage'],
    'package'       => $info['download_link'],
    'icons'         => array(),
    'banners'       => array(),
    'banners_rtl'   => array(),
    'tested'        => '',
    'requires_php'  => '',
    'compatability' => new StdClass()
  );
  return $update;
 } else {
  return false;
 }
}

function ningxia_pre_set_site_transient_update_themes( $transient ) {
 // Check for update
 $themeslug = 'Ningxia';
 $update = ningxia_check_for_update( $themeslug );
 if ( $update ) {
  $transient->response[$themeslug] = $update;
 }
 return $transient;
}
add_filter( 'pre_set_site_transient_update_themes', 'ningxia_pre_set_site_transient_update_themes' );

My build process modifies the @@@VERSION@@@ string into the current version number for the build being created (for example, 3.80.1) whereas the $info[['version']] comes from the json that been retrieved from the self-hosting site.