fix: 로또 API 504 타임아웃 및 Application error 수정

- _nas.ts: AbortSignal timeout 10s → 25s (NAS 무거운 연산 대응)
- stats/performance, report/latest, report/history: maxDuration = 60 추가 (Vercel 함수 타임아웃 연장)
- ReportTab: 에러 응답({error:"NAS_TIMEOUT"}) 받을 시 렌더 전 차단, confidence_factors null guard 추가
- PurchaseTab: API 에러 응답 감지 후 조용히 빈 상태 유지
- PatternTab: 에러 응답 감지 후 에러 메시지 표시

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

app/api/lotto/_nas.ts

@@ -15,9 +15,9 @@ function nasBase() {
   return base;
 }
 
-export async function nasGet(path: string): Promise<unknown> {
+export async function nasGet(path: string, timeoutMs = 25000): Promise<unknown> {
   const res = await fetch(`${nasBase()}${path}`, {
-    headers: nasHeaders(), signal: AbortSignal.timeout(10000),
+    headers: nasHeaders(), signal: AbortSignal.timeout(timeoutMs),
   });
   if (!res.ok) throw new Error(`NAS_${res.status}`);
   return res.json();
@@ -28,7 +28,7 @@ export async function nasPost(path: string, body: unknown): Promise<unknown> {
     method: 'POST',
     headers: { ...nasHeaders(), 'Content-Type': 'application/json' },
     body: JSON.stringify(body),
-    signal: AbortSignal.timeout(10000),
+    signal: AbortSignal.timeout(25000),
   });
   if (!res.ok) throw new Error(`NAS_${res.status}`);
   return res.json();
@@ -39,7 +39,7 @@ export async function nasPut(path: string, body: unknown): Promise<unknown> {
     method: 'PUT',
     headers: { ...nasHeaders(), 'Content-Type': 'application/json' },
     body: JSON.stringify(body),
-    signal: AbortSignal.timeout(10000),
+    signal: AbortSignal.timeout(25000),
   });
   if (!res.ok) throw new Error(`NAS_${res.status}`);
   return res.json();
@@ -47,7 +47,7 @@ export async function nasPut(path: string, body: unknown): Promise<unknown> {
 
 export async function nasDelete(path: string): Promise<unknown> {
   const res = await fetch(`${nasBase()}${path}`, {
-    method: 'DELETE', headers: nasHeaders(), signal: AbortSignal.timeout(10000),
+    method: 'DELETE', headers: nasHeaders(), signal: AbortSignal.timeout(25000),
   });
   if (!res.ok) throw new Error(`NAS_${res.status}`);
   return res.json();

app/api/lotto/report/history/route.ts

@@ -1,6 +1,8 @@
 import { NextResponse } from 'next/server';
 import { nasGet, requireSubscription, handleNasError } from '../../_nas';
 
+export const maxDuration = 60;
+
 export async function GET(request: Request) {
   try {
     const auth = await requireSubscription();

app/api/lotto/report/latest/route.ts

@@ -1,6 +1,8 @@
 import { NextResponse } from 'next/server';
 import { nasGet, requireSubscription, handleNasError } from '../../_nas';
 
+export const maxDuration = 60;
+
 export async function GET() {
   try {
     const auth = await requireSubscription();

app/api/lotto/stats/performance/route.ts

@@ -2,6 +2,8 @@ import { NextResponse } from 'next/server';
 import { createClient } from '@/lib/supabase/server';
 import { nasGet, handleNasError } from '../../_nas';
 
+export const maxDuration = 60;
+
 export async function GET() {
   try {
     const supabase = await createClient();