fix: add publish event in deleteNotificationsById and export snap t…

…ypes (#4836)

## Explanation

* What is the current state of things and why does it need to change?
The `deleteNotificationsById` doesn't fire an event with the updated
list of notifications and thus, the `updateBadge` function inside the
extension is not fired.
* What is the solution your changes offer and how does it work? Publish
an event after notifications are deleted
* Are there any changes whose purpose might not obvious to those
unfamiliar with the domain? Adding export for snap types, not able to
pull the type out directly otherwise.

### `@metamask/notification-services-controller`

- **FIX**: The `deleteNotificationsById` function did not fire an event
with the updated notifications list, this was added after the function
runs through all the notifications it needs to delete.

## Checklist

- [x] I've updated the test suite for new or updated code as appropriate
- [x] I've updated documentation (JSDoc, Markdown, etc.) for new or
updated code as appropriate
- [x] I've highlighted breaking changes using the "BREAKING" category
above as appropriate
- [x] I've prepared draft pull requests for clients and consumer
packages to resolve any breaking changes

packages/notification-services-controller/src/NotificationServicesController/NotificationServicesController.ts

@@ -1229,6 +1229,11 @@ export default class NotificationServicesController extends BaseController<
     for (const id of ids) {
       await this.deleteNotificationById(id);
     }
+
+    this.messagingSystem.publish(
+      `${controllerName}:notificationsListUpdated`,
+      this.state.metamaskNotificationsList,
+    );
   }
 
   /**

packages/notification-services-controller/src/NotificationServicesController/types/index.ts

@@ -2,3 +2,4 @@ export * from './feature-announcement';
 export * from './notification';
 export * from './on-chain-notification';
 export * from './user-storage';
+export * from './snaps/snaps';