feat: Add unread badge to sidebar for inbox view (#10803)

# Pull Request Template

## Description

This PR adds a badge to the icon in the sidebar group header and an
unread highlight for the inbox view.

## Type of change

- [x] New feature (non-breaking change which adds functionality)

## How Has This Been Tested?

**Loom video**

https://www.loom.com/share/1a880aa16de249a1836b8d014325c067?sid=87cc7b64-667b-4066-8993-d33abccf7b67


## Checklist:

- [x] My code follows the style guidelines of this project
- [x] I have performed a self-review of my code
- [x] I have commented on my code, particularly in hard-to-understand
areas
- [ ] I have made corresponding changes to the documentation
- [x] My changes generate no new warnings
- [ ] I have added tests that prove my fix is effective or that my
feature works
- [x] New and existing unit tests pass locally with my changes
- [ ] Any dependent changes have been merged and published in downstream
modules

app/javascript/dashboard/routes/dashboard/inbox/InboxList.vue

@@ -121,6 +121,7 @@ export default {
         })
         .then(() => {
           useAlert(this.$t('INBOX.ALERTS.MARK_AS_READ'));
+          this.$store.dispatch('notifications/unReadCount'); // to update the unread count in the store real time
         });
     },
     markNotificationAsUnRead(notification) {
@@ -133,6 +134,7 @@ export default {
         })
         .then(() => {
           useAlert(this.$t('INBOX.ALERTS.MARK_AS_UNREAD'));
+          this.$store.dispatch('notifications/unReadCount'); // to update the unread count in the store real time
         });
     },
     deleteNotification(notification) {
@@ -186,12 +188,16 @@ export default {
           notificationType,
         });
 
-        this.$store.dispatch('notifications/read', {
-          id,
-          primaryActorId,
-          primaryActorType,
-          unreadCount: this.meta.unreadCount,
-        });
+        this.$store
+          .dispatch('notifications/read', {
+            id,
+            primaryActorId,
+            primaryActorType,
+            unreadCount: this.meta.unreadCount,
+          })
+          .then(() => {
+            this.$store.dispatch('notifications/unReadCount'); // to update the unread count in the store real time
+          });
 
         this.$router.push({
           name: 'inbox_view_conversation',