Bitrix Sessions

Directly accessing $_SESSION breaks non-functional modes (readonly, virtual session, separated session) and tests. Use the Session API.

use Bitrix\Main\Application;

$session = Application::getInstance()->getSession();

if (!$session->has('cart'))
{
    $session->set('cart', ['items' => []]);
}

$session['cart']['items'][] = $productId;
$session['cart'] = $cart; // set via ArrayAccess