feat: Unread Count: Frontend changes for showing unread count badges (3/3)[CW-6851] (#14372)

# Pull Request Template

## Description
This is the third and final PR in a series of PRs for Introducing unread
counts in the sidebar for inboxes and labels.

In this PR:
* Added frontend changes to show the badges for unread counts for
Inboxes and Labels
* Added specs for the changes

Issue:
https://linear.app/chatwoot/issue/CW-6851/support-unread-conversation-counts



## Type of change

Please delete options that are not relevant.

- [ ] Bug fix (non-breaking change which fixes an issue)
- [x] New feature (non-breaking change which adds functionality)
- [ ] Breaking change (fix or feature that would cause existing
functionality not to work as expected)
- [ ] This change requires a documentation update

## How Has This Been Tested?

Tested this locally. Cases to test:
* Send a message from the widget and see if the count changes
* Mark a conversation as unread and see the count change for inbox
* Open an unread conversation as agent and see the count go down
* Add a label to an unread conversation from sidebar right click action
without opening the conversation and see the count of un-reads on the
label change

Added the screenshot of how it will look like

<img width="614" height="990" alt="Screenshot 2026-05-05 at 7 00 11 PM"
src="https://github.com/user-attachments/assets/99fbaa9f-bcf2-4d8d-86e2-5727f652a9dd"
/>



## Checklist:

- [x] My code follows the style guidelines of this project
- [x] I have performed a self-review of my code
- [ ] 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
- [x] 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

---------

Co-authored-by: Sojan Jose <sojan@pepalo.com>

app/javascript/dashboard/helper/specs/actionCable.spec.js

@@ -1,4 +1,4 @@
-import { describe, it, beforeEach, expect, vi } from 'vitest';
+import { describe, it, beforeEach, afterEach, expect, vi } from 'vitest';
 import ActionCableConnector from '../actionCable';
 
 vi.mock('shared/helpers/mitt', () => ({
@@ -30,12 +30,17 @@ describe('ActionCableConnector - Copilot Tests', () => {
         dispatch: mockDispatch,
         getters: {
           getCurrentAccountId: 1,
+          'accounts/isFeatureEnabledonAccount': vi.fn(() => true),
         },
       },
     };
 
     actionCable = ActionCableConnector.init(store.$store, 'test-token');
   });
+
+  afterEach(() => {
+    vi.useRealTimers();
+  });
   describe('copilot event handlers', () => {
     it('should register the copilot.message.created event handler', () => {
       expect(Object.keys(actionCable.events)).toContain(
@@ -64,4 +69,95 @@ describe('ActionCableConnector - Copilot Tests', () => {
       );
     });
   });
+
+  describe('conversation unread count event handlers', () => {
+    it('should register the conversation.unread_count_changed event handler', () => {
+      expect(Object.keys(actionCable.events)).toContain(
+        'conversation.unread_count_changed'
+      );
+      expect(actionCable.events['conversation.unread_count_changed']).toBe(
+        actionCable.onConversationUnreadCountChanged
+      );
+    });
+
+    it('should refetch unread counts when unread count changes', () => {
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+
+      expect(mockDispatch).toHaveBeenCalledWith('conversationUnreadCounts/get');
+    });
+
+    it('does not refetch unread counts when unread count feature is disabled', () => {
+      store.$store.getters[
+        'accounts/isFeatureEnabledonAccount'
+      ].mockReturnValue(false);
+
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+
+      expect(mockDispatch).not.toHaveBeenCalledWith(
+        'conversationUnreadCounts/get'
+      );
+    });
+
+    it('should throttle unread count refetches for repeated events', () => {
+      vi.useFakeTimers();
+      vi.setSystemTime(new Date('2026-01-01T00:00:00Z'));
+
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+
+      expect(mockDispatch).toHaveBeenCalledTimes(1);
+
+      vi.advanceTimersByTime(4999);
+      expect(mockDispatch).toHaveBeenCalledTimes(1);
+
+      vi.advanceTimersByTime(1);
+      expect(mockDispatch).toHaveBeenCalledTimes(2);
+      expect(mockDispatch).toHaveBeenLastCalledWith(
+        'conversationUnreadCounts/get'
+      );
+    });
+
+    it('clears pending unread count refetch before immediate refetch', () => {
+      vi.useFakeTimers();
+      vi.setSystemTime(new Date('2026-01-01T00:00:00Z'));
+
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+
+      vi.advanceTimersByTime(1000);
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+
+      vi.setSystemTime(new Date('2026-01-01T00:00:06Z'));
+      actionCable.onReceived({
+        event: 'conversation.unread_count_changed',
+        data: { account_id: 1 },
+      });
+
+      expect(mockDispatch).toHaveBeenCalledTimes(2);
+
+      vi.advanceTimersByTime(4000);
+      expect(mockDispatch).toHaveBeenCalledTimes(2);
+    });
+  });
 });