Have you used web push notifications for CRO? What were values for the key metrics? What provider did you use, if any? For your answer to be useful to all, please mention the website niche also.
I recommend to have your custom script for push notifications. If you look from a third party. There will be limit as per the plan you take.
Web push notification is an amazing way to reach your audience, clients ,users to keep them update . There are few API providers for web push notification. Though I would recommend if you develop your own application for push notification. That way you wont loose the subscribers . Taking a service from a provider have chances to loose subscribers.
Push notification is a great service that work better than e-mail marketing. From our experience push notification CTR is around 15%.