feat: @apps-in-toss/analytics 이벤트 트래킹 구현 (JSA-32)

- src/analytics.ts: initAnalytics / trackGameEvent 유틸 추가
- _app.tsx: 앱 시작 시 Analytics.init 호출
- pages/index.tsx: app_open 이벤트 (플랫폼 시간, 보유 원소 수, 골드, 강화 레벨 합계)
- FusionScreen: fusion_completed (결과 tier/name, 골드 획득, 재료 ID)
- EvolutionScreen: enhancement_completed + level_up (원소 ID/이름, 새 레벨, 비용)
- ShopScreen: item_purchased (아이템 ID/이름, 가격, 희귀도)
- OfflineRewardModal: offline_reward_claimed (오프라인 시간, 골드, 원소 종류 수)
- package.json: @apps-in-toss/analytics ^2.3.0 명시적 추가

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

pages/index.tsx

@@ -0,0 +1,61 @@
+import { css } from '@emotion/react';
+import { useEffect } from 'react';
+import { BottomTabBar } from '../src/components/BottomTabBar';
+import { OfflineRewardModal } from '../src/components/OfflineRewardModal';
+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 { useIdleTick } from '../src/hooks/useIdleTick';
+import { useGameStore } from '../src/store/useGameStore';
+import { trackGameEvent } from '../src/analytics';
+
+const rootStyle = css`
+  width: 100%;
+  height: 100vh;
+  display: flex;
+  flex-direction: column;
+  background-color: #f7f8fa;
+  overflow: hidden;
+  font-family:
+    'Pretendard',
+    -apple-system,
+    BlinkMacSystemFont,
+    sans-serif;
+`;
+
+const contentStyle = css`
+  flex: 1;
+  overflow-y: auto;
+  padding-bottom: 72px;
+`;
+
+export default function IndexPage() {
+  const { activeTab, setActiveTab, elements, gold, elementLevels } = useGameStore();
+  useIdleTick();
+
+  useEffect(() => {
+    const ownedCount = Object.values(elements).filter((c) => c > 0).length;
+    const totalLevel = Object.values(elementLevels).reduce((sum, lv) => sum + lv, 0);
+    trackGameEvent('app_open', {
+      platform: 'web',
+      platform_time: new Date().toISOString(),
+      owned_element_count: ownedCount,
+      gold,
+      total_enhance_level: totalLevel,
+    });
+  }, []);
+
+  return (
+    <div css={rootStyle}>
+      <OfflineRewardModal />
+      <div css={contentStyle}>
+        {activeTab === 'elements' && <ElementsScreen />}
+        {activeTab === 'evolution' && <EvolutionScreen />}
+        {activeTab === 'fusion' && <FusionScreen />}
+        {activeTab === 'shop' && <ShopScreen />}
+      </div>
+      <BottomTabBar activeTab={activeTab} onTabChange={setActiveTab} />
+    </div>
+  );
+}