[fix] index no-cache header to prevent stale cached page

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

app/main.py

@@ -250,4 +250,8 @@ if FRONTEND_DIR.exists():
 
     @app.get("/")
     def index() -> FileResponse:
-        return FileResponse(str(FRONTEND_DIR / "index.html"))
+        # no-cache: 브라우저가 매번 재검증하도록 강제 (구버전 HTML/JS 캐시로 인한 표시 누락 방지)
+        return FileResponse(
+            str(FRONTEND_DIR / "index.html"),
+            headers={"Cache-Control": "no-cache, max-age=0, must-revalidate"},
+        )