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/app/replay/api.py

@@ -14,6 +14,10 @@ if TYPE_CHECKING:
 
 router = APIRouter(prefix="/api", tags=["replay"])
 
+_COUNT_CONVERSATIONS_SQL = """
+SELECT COUNT(*) FROM conversations
+"""
+
 _LIST_CONVERSATIONS_SQL = """
 SELECT thread_id, created_at, last_activity, status, total_tokens, total_cost_usd
 FROM conversations
@@ -48,13 +52,22 @@ async def list_conversations(
     pool = await get_pool(request)
     offset = (page - 1) * per_page
     async with pool.connection() as conn:
+        count_cursor = await conn.execute(_COUNT_CONVERSATIONS_SQL)
+        count_row = await count_cursor.fetchone()
+        total = count_row[0] if count_row else 0
+
         cursor = await conn.execute(
             _LIST_CONVERSATIONS_SQL,
             {"limit": per_page, "offset": offset},
         )
         rows = await cursor.fetchall()
 
-    return _envelope([dict(row) for row in rows])
+    return _envelope({
+        "conversations": [dict(row) for row in rows],
+        "total": total,
+        "page": page,
+        "per_page": per_page,
+    })
 
 
 @router.get("/replay/{thread_id}")