Inject project_id into all WS broadcast data

- broadcast_message: injects project_id into message dict
- broadcast_task_event: injects project_id into task data
- chat.send handler: resolves project_id from chat or task
- _system_message: adds project_id to both task and chat broadcasts

Agents always know which project a message belongs to.

src/tracker/api/tasks.py

@@ -157,10 +157,12 @@ async def _system_message(
         created_at=task_msg.created_at.isoformat() if task_msg.created_at else now_iso,
     )
     project_id = str(task.project_id)
+    task_data = task_msg_out.model_dump()
+    task_data["project_id"] = project_id
     await manager.broadcast_message(
         project_id,
-        task_msg_out.model_dump(),
-        author_id=None,  # system has no member_id
+        task_data,
+        author_id=None,
     )
 
     # Broadcast chat message
@@ -177,7 +179,9 @@ async def _system_message(
             attachments=[],
             created_at=chat_msg.created_at.isoformat() if chat_msg.created_at else now_iso,
         )
-        await manager.broadcast_message(project_id, chat_msg_out.model_dump(), author_id=None)
+        chat_data = chat_msg_out.model_dump()
+        chat_data["project_id"] = project_id
+        await manager.broadcast_message(project_id, chat_data, author_id=None)
 
 
 async def _get_task(task_id: str, db: AsyncSession) -> Task:

src/tracker/ws/handler.py

@@ -317,12 +317,22 @@ async def _handle_chat_send(session_id: str, data: dict):
 
         msg_data = _to_message_out(msg, member).model_dump()
 
+        # Resolve project_id and inject into message data
         project_id = None
         if chat_id:
             chat_result = await db.execute(select(Chat).where(Chat.id == uuid.UUID(chat_id)))
             chat = chat_result.scalar_one_or_none()
             if chat and chat.project_id:
                 project_id = str(chat.project_id)
+        elif task_id:
+            from ..models import Task as TaskModel
+            task_result = await db.execute(select(TaskModel).where(TaskModel.id == uuid.UUID(task_id)))
+            task_obj = task_result.scalar_one_or_none()
+            if task_obj:
+                project_id = str(task_obj.project_id)
+
+        if project_id:
+            msg_data["project_id"] = project_id
             elif chat and chat.kind == ChatKind.LOBBY:
                 await manager.broadcast_all(
                     {"type": WSEventType.MESSAGE_NEW, "data": msg_data},

src/tracker/ws/manager.py

@@ -93,6 +93,9 @@ class ConnectionManager:
         - If chat_listen == "mentions": only if member_id in mention IDs
         - System messages: only if member_id in mention IDs
         """
+        # Always inject project_id into message data
+        message["project_id"] = project_id
+
         raw_mentions = message.get("mentions", [])
         # Extract member IDs from mentions (objects or strings)
         mention_ids: set[str] = set()
@@ -148,6 +151,8 @@ class ConnectionManager:
 
     async def broadcast_task_event(self, project_id: str, event_type: str, data: dict):
         """Broadcast task events. Humans get everything, agents filtered."""
+        # Always inject project_id
+        data["project_id"] = project_id
         assignee_id = data.get("assignee_id")
         reviewer_id = data.get("reviewer_id")
         watcher_ids = data.get("watcher_ids", [])