I had the opportunity to host Nuxt 3 SSR on Vercel, so this is a note for reference.

For the build settings, I needed to set the Output Directory to .output/server as follows.

For enabling CORS, the following article was helpful.

https://vercel.com/guides/how-to-enable-cors

Specifically, I was able to handle this by placing the following file at the root of the project.

{
  "headers": [
    {
      "source": "/api/(.*)",
      "headers": [
        { "key": "Access-Control-Allow-Credentials", "value": "true" },
        { "key": "Access-Control-Allow-Origin", "value": "*" },
        { "key": "Access-Control-Allow-Methods", "value": "GET,OPTIONS,PATCH,DELETE,POST,PUT" },
        { "key": "Access-Control-Allow-Headers", "value": "X-CSRF-Token, X-Requested-With, Accept, Accept-Version, Content-Length, Content-MD5, Content-Type, Date, X-Api-Version" }
      ]
    }
  ]
}

There may be incorrect descriptions, but I hope this is helpful.