403 Forbidden on /broadcasting/auth when using Laravel Echo + Pusher

I am implementing real-time broadcasting in Laravel 12 with React (Inertia) using Pusher and Laravel Echo.

The backend event fires successfully, but the frontend does not receive the broadcast. In the browser console, I consistently get the following error:

POST http://127.0.0.1:8000/broadcasting/auth 403 (Forbidden)

1. Route Where the Event Is Fired (web.php)

The event is triggered from a route using the authenticated user.

Route::get('/send-message', function () {
    $userId = auth()->id();
    $message = 'message from ' . auth()->user()->name;

    event(new MessageSent($userId, $message));

    return response()->json(['status' => 'Message sent']);
});

EvnentMessage

<?php

namespace App\Events;

use Illuminate\Broadcasting\InteractsWithSockets;
use Illuminate\Broadcasting\PrivateChannel;
use Illuminate\Contracts\Broadcasting\ShouldBroadcast;
use Illuminate\Foundation\Events\Dispatchable;
use Illuminate\Queue\SerializesModels;

class MessageSent implements ShouldBroadcast
{
    use Dispatchable, InteractsWithSockets, SerializesModels;

    public function __construct(
        public int $userId,
        public string $message
    ) {}

    public function broadcastOn(): array
    {
        return [
            new PrivateChannel('chat.' . $this->userId),
        ];
    }

    public function broadcastAs(): string
    {
        return 'MessageSent';
    }
}

Channel.php

Broadcast::channel('chat.{userId}', function ($user, $userId) {
    return true;
});

Chat.tsx

Listening the event

import { SharedData } from '@/types';
import { usePage } from '@inertiajs/react';
import { useEcho } from '@laravel/echo-react';

export default function Chat() {
    const { auth } = usePage<SharedData>().props;
    const userId = auth?.user?.id;

    useEcho(`chat.${userId}`, 'MessageSent', (e) => {
        console.log(e.message);
    });
    return <div>Check console for messages!</div>;
}

App.tsx

import { configureEcho } from '@laravel/echo-react';

configureEcho({
    broadcaster: 'pusher',
});