"static/**"をserverFilesに追記する。

{
  "version": 2,
  "builds": [
    {
      "src": "nuxt.config.js",
      "use": "@nuxtjs/vercel-builder",
      "config": {
        "serverFiles": [
          "package.json",
          "static/**" // 追記
        ]
      }
    }
  ],
  "routes": [
    { "src": "/_nuxt/.+", "headers": { "Cache-Control": "max-age=31557600" } },
    {
      "src": "/sw.js",
      "dest": "/_nuxt/static/sw.js",
      "headers": {
        "cache-control": "public, max-age=43200, immutable",
        "Service-Worker-Allowed": "/"
      }
    },
    { "src": "/(.*)", "dest": "/" }
  ]
}

参考

Deploy Nuxt with Vercel