Laravel echo private channel not working on Nuxt js

Question

I am using Laravel 9, Nuxt js, laravel-websocket. Laravel Echo is working only on public channels not working on private channels.

Here is my code.

channels.php

Broadcast::channel('trades', function ($user) {
    return auth()->check();
});

Events file (NewTrade.php)

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

    public $trade;
    public $user;

    /**
     * Create a new event instance.
     *
     * @return void
     */
    public function __construct($trade, User $user)
    {
        $this->trade = $trade;
        $this->user = $user;
    }

    /**
     * Get the channels the event should broadcast on.
     *
     * @return \Illuminate\Broadcasting\Channel|array
     */
    public function broadcastOn()
    {
        return new PrivateChannel('trades');
    }
}

nuxt.config.js

buildModules: [
    ['@nuxtjs/laravel-echo', {
        broadcaster: process.env.BROADCAST_DRIVER,
        key: process.env.PUSHER_APP_KEY,
        cluster: process.env.PUSHER_APP_CLUSTER,
        forceTLS: false,
        wsHost: '127.0.0.1',
        wsPort: 6001,
        wssPort: 6001,
        disableStats: true,
        authModule: true,
        connectOnLogin: true,
        encrypted: true,
        authEndpoint: process.env.PUSHER_AUTH_ENDPOINT,
    }]
],

echo.js (Plugin)

import Pusher from "pusher-js";

Pusher.logToConsole = true;

client echo

this.$echo.private('trades')
    .listen('NewTrade', (e) => {
        console.log("A testing");
    });

Note: If I send data from the public channel client-side received it but the only problem is when I broadcast on the private channel.

I have spent more than 10 hours and tried everything I could, but no luck. :(

Thanks.