feat(auth): add cold-start token verification with loading state to app layout

Move token verification from root layout SessionGate to (app) group layout,
enabling cold-start verification without blocking public pages (privacy/terms).
Show ActivityIndicator while verification is in progress, then redirect to
login if unverified.

BREAKING CHANGE: Authentication flow changed - token verification now occurs
in the (app) layout group instead of root layout SessionGate wrapper.

app/(app)/_layout.web.tsx

@@ -1,5 +1,5 @@
-import { useEffect } from 'react';
-import { useWindowDimensions } from 'react-native';
+import { useEffect, useState } from 'react';
+import { ActivityIndicator, View, useWindowDimensions } from 'react-native';
 import { Redirect } from 'expo-router';
 
 import { AppDesktopShell } from '../../src/app-navigation/AppDesktopShell';
@@ -7,23 +7,50 @@ import { AppRouteStack } from '../../src/app-navigation/AppRouteStack';
 import { BREAKPOINTS } from '../../src/hooks';
 import { messageManager, useAuthStore } from '../../src/stores';
 import { hrefAuthLogin } from '../../src/navigation/hrefs';
+import { useAppColors } from '../../src/theme';
 
 export default function AppLayoutWeb() {
   const { width } = useWindowDimensions();
   const isAuthenticated = useAuthStore((s) => s.isAuthenticated);
+  const fetchCurrentUser = useAuthStore((s) => s.fetchCurrentUser);
   const useDesktopShell = width >= BREAKPOINTS.desktop;
+  const colors = useAppColors();
+  const [verified, setVerified] = useState(false);
+
+  useEffect(() => {
+    // 冷启动 token 校验：仅鉴权分组 (app) 需要。
+    // 公开页（/privacy、/terms）和 (auth) 分组在根布局直接渲染，不受此校验影响。
+    fetchCurrentUser().finally(() => setVerified(true));
+  }, [fetchCurrentUser]);
 
   useEffect(() => {
     messageManager.initialize();
   }, []);
 
-  if (!isAuthenticated) {
-    return <Redirect href={hrefAuthLogin()} />;
+  // 持久化状态显示已登录则立即渲染（后台静默校验）
+  if (isAuthenticated) {
+    if (useDesktopShell) {
+      return <AppDesktopShell />;
+    }
+    return <AppRouteStack />;
   }
 
-  if (useDesktopShell) {
-    return <AppDesktopShell />;
+  // 未登录且校验未完成，显示 loading
+  if (!verified) {
+    return (
+      <View
+        style={{
+          flex: 1,
+          justifyContent: 'center',
+          alignItems: 'center',
+          backgroundColor: colors.background.default,
+        }}
+      >
+        <ActivityIndicator size="large" color={colors.primary.main} />
+      </View>
+    );
   }
 
-  return <AppRouteStack />;
+  // 校验完成仍未登录，跳转登录页
+  return <Redirect href={hrefAuthLogin()} />;
 }