How to open url in external browser on Tap on android push notifications?

Whatever you have tried so far is pretty correct. I've tried your code on a sample android app,

package com.example.notificationapp;

import androidx.appcompat.app.AppCompatActivity;
import androidx.core.app.NotificationCompat;

import android.app.NotificationChannel;
import android.app.NotificationManager;
import android.app.PendingIntent;
import android.content.Context;
import android.content.Intent;
import android.media.RingtoneManager;
import android.net.Uri;
import android.os.Build;
import android.os.Bundle;

import java.util.Random;

public class MainActivity extends AppCompatActivity {
    private static final String NOTIFICATION_CHANNEL_ID = "Notification Channel Name";
    private static final String NOTIFICATION_CHANNEL_NAME = "Notifications";

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        // Intent notificationIntent = new Intent(this, HomeActivity.class);

        Intent notificationIntent = new Intent(Intent.ACTION_VIEW);
        notificationIntent.setData(Uri.parse("https://play.google.com/store/apps/details?id=com.example.android"));
        startActivity(notificationIntent);

        notificationIntent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);
        final PendingIntent pendingIntent = PendingIntent.getActivity(this, 0, notificationIntent,
                PendingIntent.FLAG_ONE_SHOT);

        int notificationId = new Random().nextInt(60000);
//        Bitmap bitmap = getBitmapfromUrl(remoteMessage.getData().get("image-url"));

//        Intent likeIntent = new Intent(Intent.ACTION_VIEW);
//        likeIntent.putExtra(NOTIFICATION_ID_EXTRA,notificationId);
//        likeIntent.putExtra(IMAGE_URL_EXTRA, remoteMessage.getData().get("image-url"));
//        PendingIntent likePendingIntent = PendingIntent.getService(this,
//                notificationId+1,likeIntent, PendingIntent.FLAG_ONE_SHOT);


        Uri defaultSoundUri = RingtoneManager.getDefaultUri(RingtoneManager.TYPE_NOTIFICATION);
        NotificationManager notificationManager =
                (NotificationManager) getSystemService(Context.NOTIFICATION_SERVICE);


        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.O) {
            final NotificationChannel notificationChannel = new NotificationChannel(NOTIFICATION_CHANNEL_ID,
                    NOTIFICATION_CHANNEL_NAME, NotificationManager.IMPORTANCE_DEFAULT);

            notificationManager.createNotificationChannel(notificationChannel);
        }

        NotificationCompat.Builder notificationBuilder =
                new NotificationCompat.Builder(this, NOTIFICATION_CHANNEL_ID)
                        //.setLargeIcon(bitmap)
                        .setSmallIcon(R.mipmap.ic_launcher)
                        .setContentTitle("some random title")
//                        .setStyle(new NotificationCompat.BigPictureStyle()
//                                .setSummaryText("message from remote message")
//                                .bigPicture(bitmap))/*Notification with Image*/
                        .setContentText("Adding some text within content text")
                        .setAutoCancel(true)
                        .setSound(defaultSoundUri)
//                        .addAction(R.drawable.ic_favorite_true,
//                                getString(R.string.notification_add_to_cart_button),likePendingIntent)
                        .setContentIntent(pendingIntent);

        notificationManager.notify(notificationId, notificationBuilder.build());
    }
}

This is what I see,

So I see the browser is getting opened with the url specified.

I highly suspect your onMessageReceived method within MyFirebaseMessagingService is not invoked. Please add a log message within onMessageReceived and see if you are getting invoked that can possibly be the next thing to do if you haven't tried already.

I'm using this snippet and It's working well:

override fun onMessageReceived(remoteMessage: RemoteMessage) {
    super.onMessageReceived(remoteMessage)
    Log.d("TAG", "From: ${remoteMessage.from}")

    // Check if message contains a data payload.
    if (remoteMessage.data.isNotEmpty()) {
        Log.i("TAG", "Message data payload: ${remoteMessage.data}")

    }

    if (/* Check if data needs to be processed by long running job */ true) {
        handleNow(remoteMessage)
    }
    // Check if message contains a notification payload.
    remoteMessage.notification?.let {
        Log.d("TAG", "Message Notification Body: ${it.body}")
    }

    // Also if you intend on generating your own notifications as a result of a received FCM
    // message, here is where that should be initiated. See sendNotification method below.
}

private fun handleNow(remoteMessage: RemoteMessage) {
    try {
        val mBuilder =
            NotificationCompat.Builder(
                applicationContext,
                "notify_001"
            )
        var intent = Intent(Intent.ACTION_VIEW, Uri.parse(
                        "market://details?id=" + applicationContext.packageName))
        intent.action = "Unique_id"
        intent.flags = Intent.FLAG_ACTIVITY_SINGLE_TOP
        val pendingIntent = PendingIntent.getActivity(
            applicationContext, 0, intent,
            PendingIntent.FLAG_UPDATE_CURRENT
        )

        val bigText =
            NotificationCompat.BigTextStyle()

        for (item in remoteMessage.data.keys) {
            Log.i("TAG", "Key:" + item + " " + remoteMessage.data[item])
        }
        if (remoteMessage.data["big_text"] != null) {
            bigText.bigText(remoteMessage.data["big_text"])
        }
        if (remoteMessage.data["big_content_title"] != null) {
            bigText.setBigContentTitle(remoteMessage.data["big_content_title"])
        }
        if (remoteMessage.data["summary_text"] != null) {
            bigText.setBigContentTitle(remoteMessage.data["summary_text"])
        }a
        mBuilder.setContentIntent(pendingIntent)
        mBuilder.setContentTitle(remoteMessage.notification?.title)
        mBuilder.setContentText(remoteMessage.notification?.body)
        mBuilder.priority = NotificationCompat.PRIORITY_MAX
        mBuilder.setAutoCancel(true)
        mBuilder.setContentIntent(pendingIntent)
        val bitmap =
            BitmapFactory.decodeResource(
                applicationContext.getResources(),
                R.drawable.chandmahame_logo
            )
        mBuilder.setSmallIcon(R.mipmap.ic_launcher).setLargeIcon(bitmap)
        mBuilder.setStyle(bigText)
        val mNotificationManager: NotificationManager = applicationContext
            .getSystemService(Context.NOTIFICATION_SERVICE) as NotificationManager

        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.O) {
            val channelId = "1234"
            val channel = NotificationChannel(
                channelId, "YOUR_CHANNEL_ID",
                NotificationManager.IMPORTANCE_HIGH
            )
            mNotificationManager.createNotificationChannel(channel)
            mBuilder.setChannelId(channelId)
        }

        mNotificationManager.notify(
            NOTIFICATION_ID,
            mBuilder.build()
        )
    } catch (e: Exception) {
        e.printStackTrace()
    }
}

and for sure, using it as Java code is not a big deal.

I search in tutorialpoint.com and appear this with a button, maybe can help.

Intent i = new Intent(Intent.ACTION_VIEW);
i.setData(Uri.parse(url));
startActivity(i);