spec: update api consistency

Align optimistic locking conflict payload, update websocket docs, and adjust tests.

backend/app/api/tasks/router.py

@@ -407,10 +407,13 @@ async def update_task(
         if task_data.version != task.version:
             raise HTTPException(
                 status_code=status.HTTP_409_CONFLICT,
-                detail=(
-                    f"Version conflict: current_version={task.version}, "
-                    f"provided_version={task_data.version}"
-                ),
+                detail={
+                    "error": "conflict",
+                    "message": "Task has been modified by another user. Please refresh and retry.",
+                    "current_version": task.version,
+                    "provided_version": task_data.version,
+                    "your_version": task_data.version,
+                },
             )
 
     # Capture old values for audit and triggers

backend/app/api/websocket/router.py

@@ -168,7 +168,6 @@ async def websocket_notifications(
        - Connect with: ws://host/ws/notifications?token=<jwt_token>
 
     Messages sent by server:
-    - {"type": "auth_required"}  - Sent when waiting for auth message
     - {"type": "connected", "data": {"user_id": "...", "message": "..."}}  - Connection success
     - {"type": "unread_sync", "data": {"notifications": [...], "unread_count": N}}  - All unread on connect
     - {"type": "notification", "data": {...}}  - New notification
@@ -356,7 +355,6 @@ async def websocket_project_sync(
        - Connect with: ws://host/ws/projects/{project_id}?token=<jwt_token>
 
     Messages sent by server:
-    - {"type": "auth_required"}  - Sent when waiting for auth message
     - {"type": "connected", "data": {"project_id": "...", "user_id": "..."}}
     - {"type": "task_created", "data": {...}, "triggered_by": "..."}
     - {"type": "task_updated", "data": {...}, "triggered_by": "..."}