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/conversations/index.js

@@ -258,7 +258,11 @@ export const mutations = {
         emitter.emit(BUS_EVENTS.SCROLL_TO_MESSAGE);
       }
     } else {
-      _state.allConversations.push(conversation);
+      const { conversationType } = _state.conversationFilters || {};
+      const { MENTION, PARTICIPATING } = wootConstants.CONVERSATION_TYPE;
+      if (![MENTION, PARTICIPATING].includes(conversationType)) {
+        _state.allConversations.push(conversation);
+      }
     }
   },