Add config forms to existing admin page Instead of creating a new route and menu:

  amustatuscode.config:
  path: '/admin/config/statuscode/config'
  defaults:
    _form: '\Drupal\amu_http_status_code_display\Form\AmuHttpStatusCodeDisplayConfigForm'
    _title: 'HTTP status code error messages'
  requirements:
    _permission: 'administer http status code'


amustatuscode.config:
  title: 'AMU HTTP status code'
  description: 'Customize HTTP status code error messages'
  parent: system.admin_config
  route_name: amustatuscode.config
  weight: 100


How can I add this form to the existing basic site settings?


  /admin/config/system/site-information
You could extend the default form by using a Route subscriber.
To do so, create a file named RouteSubscriber.php whithin your module in a src/Routing folder.

the file should look like this:

&lt;?php 
namespace Drupal\YOUR_MODULE\Routing;

use Drupal\Core\Routing\RouteSubscriberBase;
use Symfony\Component\Routing\RouteCollection;

/**
 * Listens to the dynamic route events.
 */
class RouteSubscriber extends RouteSubscriberBase {

  /**
   * {@inheritdoc}
   */
  protected function alterRoutes(RouteCollection $collection) {
    if ($route = $collection-&gt;get('system.site_information_settings')) 
      $route-&gt;setDefault('_form', 'Drupal\YOUR_MODULE\Form\ExtendedSiteInformationForm');
  }

}


You should then create a ExtendedSiteInformationForm.php file within your module src/Form folder like that:

&lt;?php

namespace Drupal\YOUR_MODULE\Form;

use Drupal\Core\Form\FormStateInterface;
use Drupal\system\Form\SiteInformationForm;


class ExtendedSiteInformationForm extends SiteInformationForm {

   /**
   * {@inheritdoc}
   */
  public function buildForm(array $form, FormStateInterface $form_state) {
   $form=  parent::buildForm($form, $form_state);
   //update your $form...
   return $form;
}
}


This way you won't need your routing.yml file anymore.