feat: 프레스티지/업적 UI 컴포넌트 추가 및 게임 상태 업데이트 (JSA-55)

- AchievementToast, PrestigeModal, AchievementsScreen 컴포넌트 추가
- BottomTabBar에 업적 탭 연결
- useGameStore 프레스티지/업적 상태 로직 수정
- pages/index.tsx 라우팅 업데이트

Co-Authored-By: Paperclip <noreply@paperclip.ing>

pages/index.tsx

@@ -2,10 +2,12 @@ import { css } from '@emotion/react';
 import { useEffect } from 'react';
 import { BottomTabBar } from '../src/components/BottomTabBar';
 import { OfflineRewardModal } from '../src/components/OfflineRewardModal';
+import { AchievementToast } from '../src/components/AchievementToast';
 import { ElementsScreen } from '../src/components/screens/ElementsScreen';
 import { EvolutionScreen } from '../src/components/screens/EvolutionScreen';
 import { FusionScreen } from '../src/components/screens/FusionScreen';
 import { ShopScreen } from '../src/components/screens/ShopScreen';
+import { AchievementsScreen } from '../src/components/screens/AchievementsScreen';
 import { SettingsScreen } from '../src/components/screens/SettingsScreen';
 import { useIdleTick } from '../src/hooks/useIdleTick';
 import { useGameStore } from '../src/store/useGameStore';
@@ -50,11 +52,13 @@ export default function IndexPage() {
   return (
     <div css={rootStyle}>
       <OfflineRewardModal />
+      <AchievementToast />
       <div css={contentStyle}>
         {activeTab === 'elements' && <ElementsScreen />}
         {activeTab === 'evolution' && <EvolutionScreen />}
         {activeTab === 'fusion' && <FusionScreen />}
         {activeTab === 'shop' && <ShopScreen />}
+        {activeTab === 'achievements' && <AchievementsScreen />}
         {activeTab === 'settings' && <SettingsScreen />}
       </div>
       <BottomTabBar activeTab={activeTab} onTabChange={setActiveTab} />