[ Plugin ajax and session ] Using admin_ajax remove session

Hello!

I am trying to use ajax to add product in a session cart in a custom plugin (this is my first plugin dev).

In the plugin file, I have started the session:

function session_manager() {
	    if (!session_id()) {
	        session_start();
	    }
	}
	add_action('init', 'session_manager',1);

I have then added the js to the page using the wp_enqueue_script function and the wp_localize_script:

function add_ld_advanced_cart_js() {
		wp_enqueue_script(
			'ld-advanced-cart',
			LD_PLUGIN_JS_URL,
			array('jquery')
		);

		// declare the URL to the file that handles the AJAX request (wp-admin/admin-ajax.php)
		wp_localize_script( 'ld-advanced-cart', 'MyAjax', array(
			'ajaxurl' => admin_url( 'admin-ajax.php' )
			)
		);

	}
	/* add javascript to page using this plugin */
	add_action('wp_enqueue_scripts', 'add_ld_advanced_cart_js');

I have defined the 2 ajax action:

add_action( 'wp_ajax_nopriv_add-to-cart-submit', 'ajax_addtocart_submit' );
add_action( 'wp_ajax_add-to-cart-submit', 'ajax_addtocart_submit' );

But from the ajax_addtocart_submit, I do not have access to current session variable values, even if I add in this function:

if( !session_id())
    session_start();

If I use use my own ajax php file (not going through admin_ajax.php), this is working well.

Did I miss something to make the SESSION available in the ajax part or it’s just not possible in the way WordPress is built??

Thx in advance!