Yes, slack notifications feature is in our future plans. However, we will only make slack notifications and webhooks available in the business plan.
Moreover, we are also working on custom intervals for admin email notifications (Ex: instant, daily, weekly). At this moment, there's a delay of 15 minutes to prevent sending thousands of email to websites that gets comments each minute. And, you won't receive an email if you are active in the console when a user publishes a comment. I'm think that's the reason you didn't get email notifications.