feat(chat): implement external browser prompt logic and update tests

src/app/chat/chat-screen.tsx

@@ -28,7 +28,7 @@ import {
 } from "./chat-image-overlay-url";
 import {
   deriveIsGuest,
-  isChatDevelopmentEnvironment,
+  shouldStartExternalBrowserPrompt,
 } from "./chat-screen.helpers";
 import { useFirstRechargeOfferBanner } from "./hooks/use-first-recharge-offer-banner";
 import { useChatUnlockNavigationFlow } from "./hooks/use-chat-unlock-navigation-flow";
@@ -90,6 +90,11 @@ export function ChatScreen() {
     loginStatus: authState.loginStatus,
   });
   const shouldShowPwaInstall = state.historyLoaded && state.messages.length >= 10;
+  const shouldShowBrowserHint = shouldStartExternalBrowserPrompt({
+    hasInitialized: authState.hasInitialized,
+    isLoading: authState.isLoading,
+    loginStatus: authState.loginStatus,
+  });
 
   useChatGuestLogin({
     dispatch: authDispatch,
@@ -186,7 +191,7 @@ export function ChatScreen() {
         </div>
 
         {/* 浏览器提示（应用内浏览器检测） */}
-        <BrowserHintOverlay forceShow={isChatDevelopmentEnvironment()} />
+        {shouldShowBrowserHint ? <BrowserHintOverlay forceShow /> : null}
 
         {/* PWA 安装提示触发器（聊天消息数量达到阈值后才允许弹出） */}
         <PwaInstallOverlay enabled={shouldShowPwaInstall} />