Admin submenu does not call function to load the page

Context

I’m making a big plugin with a complex architecture. I would like in my plugin architecture split pages and menus building on admin side.

So I have these classes : Menu.php, Submenu.php and Page.php, SubPage.php

I would like, when the administrator clik on menu/submenu links, it runs a common function callback inside Menu.php and Submenu.php which load only the right page or subpage thanks $_GET['page'].

Problem

Each submenu link does not bind a subpage anymore.

All href of submenu links are in this format :

https://my-site.org/wp-admin/my-slug-page

instead of :

https://my-site.org/wp-admin/admin.php?page=my-slug-page

Submenu.php

class SubMenu { 

    public $parent_slug;

    public $page_title;

    public $menu_title;

    public $capability;

    public $menu_slug;

    public $priority;


   public function __construct( $parent_slug, $page_title, $menu_title, $capability, $menu_slug, $priority = 10 ) {
       $this->parent_slug = $parent_slug;
       $this->page_title = $page_title;
       $this->menu_title = $menu_title;
       $this->capability = $capability;
       $this->menu_slug = $menu_slug;
       $this->priority = $priority;

       // Initialize the component
       add_action( 'admin_menu', array( $this, 'add_submenu' ), $this->priority );
   }


   public function add_submenu() {

        $page_hook = add_submenu_page(
             $this->parent_slug, 
             _x( $this->page_title, "page_title", PLUGIN_DOMAIN ), 
             _x( $this->menu_title, "menu_title", PLUGIN_DOMAIN ), 
             $this->capability, 
             $this->menu_slug, 
             array( $this, "output_rooter" ) 
        );

   }

   public function output_rooter(){
        // check $_GET['page'] value
        ...
        // Load the right SubPage class with the view
        $class = strToKamelCase( $_GET['page'] );
        new $class(); //<-- extends SubPage.php
        ... 
   }



}

The function output_rooter is never called and I have a 404 error each time I click on a submenu link.

Notice : with menu links it works correctly and all href links are perfect.

Someone has got an idea what it should be ?