Symfony 5 Private chat with Pusher

I've created a simple group chat application with Symfony 5, and now I'm trying to add Socket with Pusher.

For the moment it's working, but because I'm using a single channel, everytime a user post a message, this message appears on every conversation. That's why I would like to pass the messaging_id in the channel name, but it's not working.

I read on the doc I should use the prefix private- in my channel name, but with this the console is asking me to auth the user, and I don't know how do it because my user is already connected.

Here is my logic controller :

 // Pusher
        $options = array(
            'cluster' => 'eu',
            'useTLS' => true
        );
        $pusher = new Pusher(
            'ba75523bee28d7c644f2',
            '9597b6daf0fb4e20fda2',
            '1266737',
            $options
        );

        //New message
        $message = new Message();
        $form = $this->createForm(MessageType::class, $message);
        $form->handleRequest($request);

        if ($form->isSubmitted() && $form->isValid()) {
            $message->setAuthor($user);
            $message->setMessaging($messaging);
            $entityManager = $this->getDoctrine()->getManager();
            $entityManager->persist($message);
            $entityManager->flush();

            $data = $message->getContent();

            if ($pusher->trigger('my-channel', 'my_event', $data)) {
                echo 'success';
            } else {
                header('', true, 403);
                echo 'error';
            }

            return new JsonResponse(Response::HTTP_OK);
        }

Here is my Javascript :

Pusher.logToConsole = true;

var pusher = new Pusher('ba75523bee28d7c644f2', {
    cluster: 'eu',
});

var channel = pusher.subscribe('my-channel');

channel.bind('my_event',
    function (data) {
        console.log(data);
        $('.lala').append('<li class = "chat-left"><div class="chat-text">' + data + '</div>');
    });

channel.bind('pusher:subscription_succeeded', function (members) {
    console.log('successfully subscribed!');
});

function ajaxCall(ajax_url, ajax_data) {
    $.ajax({
        type: "POST",
        url: ajax_url,
        dataType: "json",
        data: ajax_data,
        success: function (response) {
            console.log(response);
        },
        error: function (msg) { }
    });
}

Here is the error if I use the private- prefix : enter image description here

To summarize, I would like every message to only appear in the good conversation (Messages are of course saved in the database in the right conversation). Thank you for your help !