You can send notifications to your service worker using push notification API . You can send notifications to a react app using the service worker mechanism. You can get a service worker pre-configured by generating the code with Create React App. More details about CRA service-worker here.

 `npx create-react-app my-app --template cra-template-pwa`. 

In order to add push notifications you will need to implement a listener inside your business logic that will trigger the notification (a processing result, a button push... etc) then you can trigger the notification as mentioned here.

check the documentation : https://developers.google.com/web/ilt/pwa/introduction-to-push-notifications

In order for notifications to appear when the app isn't open, you'll need to use Web Push as well. Web push allows you to send a notification from your server to device. When the push arrives on the device, it wakes up the service worker, and the notification is shown there.

Instructions for setting up Web Push & Notifications are available at https://developers.google.com/web/fundamentals/push-notifications