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/featureFlags.js

@@ -46,6 +46,7 @@ export const FEATURE_FLAGS = {
   COMPANIES: 'companies',
   ADVANCED_SEARCH: 'advanced_search',
   CONVERSATION_REQUIRED_ATTRIBUTES: 'conversation_required_attributes',
+  CONVERSATION_UNREAD_COUNTS: 'conversation_unread_counts',
 };
 
 export const PREMIUM_FEATURES = [