すべてのapiでCORSが有効になります。POSTメソッドを使う場合は、OPTIONSも追加必要かもです

vercel.json

{
  "headers": [
      {
        "source": "/(.*)",
        "headers": [
          { "key": "Access-Control-Allow-Origin", "value": "*" },
          { "key": "Access-Control-Allow-Methods", "value": "*" },
          { "key": "Access-Control-Allow-Headers", "value": "*" }
        ]
      }
  ]
}

hello.js

export async function POST(request) {
    return new Response()
}

export async function OPTIONS() {
    return new Response()
}