refactor: 'SITE_ID' 환경변수 쿠키로 수정

apps/common/features/app/api/proxy/[...url]/route.ts

@@ -4,7 +4,6 @@ import {
   CLAIM_NAME,
   REFRESH_TOKEN,
   SERVER_API_URL,
-  SITE_ID,
 } from "@/shared/config";
 import { cookies } from "next/headers";
 import { NextResponse } from "next/server";
@@ -15,9 +14,10 @@ async function handler(
   method: "GET" | "POST" | "PUT" | "DELETE",
 ) {
   const cookieStore = await cookies();
+  const siteId = cookieStore.get("site-id-key")?.value ?? "";
   const headers: Record<string, string> = {
     "Content-Type": "application/json",
-    "X-Site-Id": SITE_ID,
+    "X-Site-Id": siteId,
   };
   let body = {};
   const isRefreshHandler = params.url.includes("refresh");