full code:

mocks/http.ts

import { createMiddleware } from '@mswjs/http-middleware';
import express from 'express';
import cors from 'cors';
import { handlers } from './handlers';

const app = express();
const port = 9090;

app.use(cors({ origin: 'http://localhost:3000', optionsSuccessStatus: 200, credentials: true }));
app.use(express.json());
app.use(createMiddleware(...handlers));
app.listen(port, () => console.log(`Mock server is running on port: ${port}`));

package.json

{
  "scripts": {
    "dev": "next dev",
    "mock": "npx tsx ./mocks/http.ts",
  }
}

axios settings:

axios.defaults.baseURL = 'http://localhost:9090';

start mock server yarn mock, start dev server yarn dev