chore: Enable Participating tab for conversations (#11714)

## Summary

This PR enables the **Participating** conversation view in the main
sidebar and keeps the behavior aligned with existing conversation views.

## What changed

- Added **Participating** under Conversations in the new sidebar.
- Added a guard in conversation realtime `addConversation` flow so
generic `conversation.created` events are not injected while the user is
on Participating view.
- Added participating route mapping in conversation-list redirect helper
so list redirects resolve correctly to `/participating/conversations`.

## Scope notes

- Kept changes minimal and consistent with current `develop` behavior.
- No additional update-event filtering was added beyond what existing
views already do.

---------


Co-authored-by: Sivin Varghese <64252451+iamsivin@users.noreply.github.com>
Co-authored-by: iamsivin <iamsivin@gmail.com>

app/javascript/dashboard/store/modules/specs/conversations/mutations.spec.js

@@ -786,9 +786,55 @@ describe('#mutations', () => {
       });
     });
 
-    it('should add conversation if not found', () => {
+    it('should add conversation if not found on normal view', () => {
       const state = {
         allConversations: [],
+        conversationFilters: {},
+      };
+
+      const conversation = {
+        id: 1,
+        status: 'open',
+      };
+
+      mutations[types.UPDATE_CONVERSATION](state, conversation);
+      expect(state.allConversations).toEqual([conversation]);
+    });
+
+    it('should not add conversation if not found on participating view', () => {
+      const state = {
+        allConversations: [],
+        conversationFilters: { conversationType: 'participating' },
+      };
+
+      const conversation = {
+        id: 1,
+        status: 'open',
+      };
+
+      mutations[types.UPDATE_CONVERSATION](state, conversation);
+      expect(state.allConversations).toEqual([]);
+    });
+
+    it('should not add conversation if not found on mention view', () => {
+      const state = {
+        allConversations: [],
+        conversationFilters: { conversationType: 'mention' },
+      };
+
+      const conversation = {
+        id: 1,
+        status: 'open',
+      };
+
+      mutations[types.UPDATE_CONVERSATION](state, conversation);
+      expect(state.allConversations).toEqual([]);
+    });
+
+    it('should add conversation if not found on unattended view', () => {
+      const state = {
+        allConversations: [],
+        conversationFilters: { conversationType: 'unattended' },
       };
 
       const conversation = {