feat(web): 聊天请求携带行为模式 mode(A3) — useChat 读当前 mode 经 REST 发送

- api.ts chatStream 新增可选 mode，空则不写键(后端回落chat)
- useChat.ts 发送时带上 useModeStore 当前 mode，使非chat模式消息在Web端真正落库
- 修正 docblock(移除虚构的WS chat回退描述)

frontend/web/src/lib/api.ts

@@ -248,15 +248,24 @@ export function chatSync(
  *  `image` (a base64 data: URI or URL) is attached for the vision path; the
  *  gateway's chat body currently has no image field, so an unconfigured backend
  *  simply ignores it. `deviceId` mirrors the client's per-browser id onto the
- *  persisted message (design/16 §4.5). */
+ *  persisted message (design/16 §4.5). `mode` is the behavior mode this turn is
+ *  sent in (design/01 §3); omitted when empty so the backend falls back to chat. */
 export function chatStream(
   sessionId: string,
   text: string,
-  image?: string
+  image?: string,
+  mode?: Mode
 ): Promise<{ stream: true }> {
   return request<{ stream: true }>("/chat", {
     method: "POST",
-    body: JSON.stringify({ sessionId, text, image, stream: true, deviceId: getClientId() }),
+    body: JSON.stringify({
+      sessionId,
+      text,
+      image,
+      stream: true,
+      deviceId: getClientId(),
+      ...(mode ? { mode } : {}),
+    }),
   });
 }