How to implement the WordPress REST API with a React UI in such a way that the API endpoints are hidden behind a proxy URL

Question

How to implement the WordPress REST API with a React UI in such a way that the API endpoints are hidden behind a proxy URL.

I have tried many options like: 1)

const proxy = require('http-proxy');

const proxyUrl = 'http://localhost/mywebsite/wp-json/wp/v2/';

const app = proxy.createServer({
  target: proxyUrl,
});

app.listen(3000);

and 2)

const { createProxyMiddleware } = require('http-proxy-middleware');

module.exports = function(app) {
  app.use(
    '/api',
    createProxyMiddleware({
      target: 'http://localhost/mywebsite/wp-json'
      changeOrigin: true,
    })
  );
};

I am getting errors { "code": "rest_no_route", "message": "No route was found matching the URL and request method.", "data": { "status": 404 } }

instead of API response

Please help me out get the solution for this.