fix(mobile): change update check interval from 24h to 30-90s random

Allows faster detection of urgent updates while preventing excessive
API calls with random cooldown period.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/mobile-app/lib/features/home/presentation/pages/home_shell_page.dart

@@ -1,3 +1,4 @@
+import 'dart:math';
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
 import 'package:go_router/go_router.dart';
@@ -18,11 +19,8 @@ class HomeShellPage extends ConsumerStatefulWidget {
 
 class _HomeShellPageState extends ConsumerState<HomeShellPage>
     with WidgetsBindingObserver {
-  /// 上次检查更新的时间
-  static DateTime? _lastCheckTime;
-
-  /// 检查间隔（24小时）
-  static const _checkInterval = Duration(hours: 24);
+  /// 下次允许检查更新的时间
+  static DateTime? _nextCheckAllowedTime;
 
   @override
   void initState() {
@@ -51,10 +49,11 @@ class _HomeShellPageState extends ConsumerState<HomeShellPage>
   Future<void> _checkForUpdateIfNeeded() async {
     final now = DateTime.now();
 
-    // 如果从未检查过，或者距上次检查超过24小时，则检查
-    if (_lastCheckTime == null ||
-        now.difference(_lastCheckTime!) > _checkInterval) {
-      _lastCheckTime = now;
+    // 如果从未检查过，或者已过冷却时间，则检查
+    if (_nextCheckAllowedTime == null || now.isAfter(_nextCheckAllowedTime!)) {
+      // 设置下次允许检查时间（30-90秒随机间隔）
+      final randomSeconds = 30 + Random().nextInt(61); // 30 + 0~60 = 30~90
+      _nextCheckAllowedTime = now.add(Duration(seconds: randomSeconds));
       await checkForAppUpdate(context);
     }
   }