Implement real-time WebSocket gateway for presence, DM, and world chat (US-4, US-2)

backend/app/routers/chat_dm.py

@@ -81,6 +81,7 @@ from app.models.chat import Conversation, ConversationParticipant, Message
 from app.models.social import Block
 from app.models.user import User
 from app.rate_limit import rate_limit
+from app.services.chat_pubsub import publish_dm_chat_event
 from app.services.text_filter import FilterAction, default_text_filter
 
 router = APIRouter()
@@ -264,7 +265,9 @@ async def send_dm(
     await db.commit()
     await db.refresh(message)
 
-    return _to_message_response(message, recipient_id=user_id)
+    resp = _to_message_response(message, recipient_id=user_id)
+    await publish_dm_chat_event(conversation.id, resp.model_dump(mode="json"))
+    return resp
 
 
 @router.get("/{user_id}/messages", response_model=DMMessageListResponse)