[cs] feat: 로그인 시 X-Device-Id 헤더 추가

apps/cs/app/api/proxy/[...url]/route.ts

@@ -1,3 +1,6 @@
+import { cookies } from "next/headers";
+import { NextResponse } from "next/server";
+
 import {
   ACCESS_TOKEN,
   AUTH_USER_ID,
@@ -7,8 +10,6 @@ import {
   SERVER_API_URL,
   SITE_ID,
 } from "@/shared/config";
-import { cookies } from "next/headers";
-import { NextResponse } from "next/server";
 
 async function handler(
   request: Request,
@@ -20,6 +21,10 @@ async function handler(
     "Content-Type": "application/json",
     "X-Site-Id": SITE_ID,
   };
+  const deviceId = request.headers.get("X-Device-Id");
+  if (deviceId) {
+    headers["X-Device-Id"] = deviceId;
+  }
   let body = {};
   const isRefreshHandler = params.url.includes("refresh");