Customize Push Notification

Good morning, I am creating a site for a pizzeria and I need to know if it is possible to send a custom push notification to a specific user. This is so that when the user proceeds with the order I can inform him via push notification of the acceptance of his order or the change of delivery time…

I need that from the back end of woocommerce, or from the back end of wordpress, I have the ability to send a custom notification.

And if this notification is mobile frendly.

Thanks for your availability