feat: wire frontend pages to live APIs and standardize response contracts (P1)

- Backend: Add COUNT query and paginated response shape to conversations endpoint
  Returns { conversations: [...], total, page, per_page } instead of flat array
- Frontend: Replace mock data in DashboardPage with fetchAnalytics() API calls
- Frontend: Replace mock data in ReplayListPage with fetchConversations() API calls
- Frontend: Replace mock data in ReplayPage with fetchReplay() API calls
- Add proper loading, empty, and error states to all three pages
- Align ConversationSummary type with actual DB columns (created_at, status)
- Update unit and E2E tests for new paginated conversation response shape
- Add fetchone() to FakeCursor for COUNT query support in E2E tests

backend/tests/e2e/test_replay_analytics.py

@@ -44,6 +44,8 @@ class ReplayPool(FakePool):
         async def execute(self, query: str, params=None):
             from tests.e2e.conftest import FakeCursor
 
+            if "COUNT" in query and "conversations" in query:
+                return FakeCursor([(len(self._convos),)])
             if "conversations" in query and "SELECT" in query:
                 return FakeCursor(self._convos)
             if "checkpoints" in query:
@@ -94,9 +96,11 @@ class TestFlow6ReplayConversation:
             assert resp.status_code == 200
             body = resp.json()
             assert body["success"] is True
-            assert len(body["data"]) == 2
-            assert body["data"][0]["thread_id"] == "conv-001"
-            assert body["data"][1]["thread_id"] == "conv-002"
+            data = body["data"]
+            assert len(data["conversations"]) == 2
+            assert data["conversations"][0]["thread_id"] == "conv-001"
+            assert data["conversations"][1]["thread_id"] == "conv-002"
+            assert data["total"] == 2
 
     def test_list_conversations_pagination(self) -> None:
         conversations = [
@@ -206,7 +210,8 @@ class TestFullUserJourney:
             body = resp.json()
             assert body["success"] is True
             assert any(
-                c["thread_id"] == "e2e-journey-1" for c in body["data"]
+                c["thread_id"] == "e2e-journey-1"
+                for c in body["data"]["conversations"]
             )
 
             # Step 3: Health check still works