Why does react-router not works at vercel?

Add a vercel.json file at the root of your project, and use “rewrites” to rewrite all incoming paths to refer to your index path.

For example:

{
  "rewrites":  [
    {"source": "/(.*)", "destination": "/"}
  ]
}

Check here for further information: https://vercel.com/docs/configuration#project/rewrites