fix: 跨端消息同步 — 用户消息广播 + 会话隔离 + 去重

后端: handleChatMessage 将用户消息通过 broadcastToUser 广播给同用户所有设备
协议: ClientMessage 新增 ClientMsgID 字段用于跨端去重
前端: 发送消息时携带 client_msg_id，收到回显时跳过本地已添加的消息
前端: handleServerMessage 新增 session_id 过滤，防止不同会话消息串扰

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

backend/gateway/internal/handler/chat_handler.go

@@ -168,8 +168,12 @@ func (h *ChatHandler) handleChatMessage(client *ws.Client, msg ws.ClientMessage)
 	}
 
 	// 缓存用户消息（在 goroutine 前完成，避免竞态）
+	userMsgID := msg.ClientMsgID
+	if userMsgID == "" {
+		userMsgID = "msg_" + generateID()
+	}
 	userMsg := ws.Message{
-		ID:        "msg_" + generateID(),
+		ID:        userMsgID,
 		Role:      "user",
 		Content:   msg.Content,
 		Timestamp: time.Now().UnixMilli(),
@@ -183,6 +187,21 @@ func (h *ChatHandler) handleChatMessage(client *ws.Client, msg ws.ClientMessage)
 	}
 	h.hub.CacheMessage(client.UserID, client.SessionID, userMsg)
 
+	// 广播用户消息给同用户所有设备（跨端同步）
+	h.broadcastToUser(client.UserID, ws.ServerMessage{
+		Type:      "response",
+		MessageID: userMsgID,
+		Content:   msg.Content,
+		Role:      "user",
+		MsgType:   "chat",
+		SessionID: client.SessionID,
+		Timestamp: time.Now().UnixMilli(),
+		ClientInfo: &ws.ClientInfo{
+			ClientID:   client.ClientID,
+			DeviceName: client.DeviceName,
+		},
+	})
+
 	// 在 goroutine 中进行 AI-Core 调用和流式发送，避免阻塞 ReadPump
 	go h.streamResponse(client, mode, reqBody, msg.Content)
 }