Repository: next.js
Issue: Page Router with Next 14 and 'use client' does not work with cypress 12.3.0
Labels: bug

### Link to the code that reproduces this issue

https://github.com/eduardo-villasboas/with-cypress-app

# I am getting the error when running next with cypress. 

### To Reproduce

## There are two manners to reproduces the error

### Using https://www.npmjs.com/package/start-server-and-test
 
1. Run ```npm run e2e:headless``` this command will start next in dev mode and run e2e tests using https://www.npmjs.com/package/start-server-and-test

### Running next server manually

1. ```rm .next -rf``` 
2. ```rm node_modules/ -rf```
3. ```npm install```
4. ```npm run build```
5. ```npm run dev```
6. and in another terminal ```npx cypress run --e2e```

***Note that the errors don't happen always and in the second approach, running manually I got the error in the first executions after deleting the paths .next and node_modules/. In the repo https://github.com/eduardo-villasboas/with-cypress-app, I create two branches next-14-with-app-routing-error-tests and next-14-with-pages-routing-sucess-tests, because I have discovered this error occurs only when using the new nextjs routing system and accessing an component using 'use client' ***



### Current vs. Expected behavior

Test app.cy.ts should pass

But I getting the following error. I am attaching a video that the own cypress have recorded.

```bash
  1) Navigation
       should navigate to the about page:
     TypeError: The following error originated from your application code, not from Cypress.

  > __webpack_require__.n is not a function

When Cypress detects uncaught errors originating from your application it will automatically fail the current test.

This behavior is configurable, and you can choose to turn this off by listening to the `uncaught:exception` event.

https://on.cypress.io/uncaught-exception-from-application
      at eval (webpack-internal:///app-pages-browser/./app/about/page.tsx:7:108)
      at <unknown> (app-pages-browser/./app/about/page.tsx http://localhost:3000/_next/static/chunks/app/about/page.js:38:1)
      at options.factory (http://localhost:3000/_next/static/chunks/webpack.js?v=1699211960328:704:31)
      at __webpack_require__ (http://localhost:3000/_next/static/chunks/webpack.js?v=1699211960328:37:33)
      at fn (http://localhost:3000/_next/static/chunks/webpack.js?v=1699211960328:359:21)
      at requireModule (webpack-internal:///app-pages-browser/./node_modules/next/dist/compiled/react-server-dom-webpack/cjs/react-server-dom-webpack-client.browser.development.js:156:23)
      at initializeModuleChunk (webpack-internal:///app-pages-browser/./node_modules/next/dist/compiled/react-server-dom-webpack/cjs/react-server-dom-webpack-client.browser.development.js:1357:17)
      at resolveModuleChunk (webpack-internal:///app-pages-browser/./node_modules/next/dist/compiled/react-server-dom-webpack/cjs/react-server-dom-webpack-client.browser.development.js:1302:5)
      at eval (webpack-internal:///app-pages-browser/./node_modules/next/dist/compiled/react-server-dom-webpack/cjs/react-server-dom-webpack-client.browser.development.js:1774:14)
```



https://github.com/vercel/next.js/assets/57238282/8384e8de-6d48-4fd5-aeb6-ae2e5b89aec0





### Verify canary release

- [X] I verified that the issue exists in the latest Next.js canary release

### Provide environment information

```bash
Operating System:
  Platform: linux
  Arch: x64
  Version: #26~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Thu Jul 13 16:27:29 UTC 2
Binaries:
  Node: 20.9.0
  npm: 10.1.0
  Yarn: N/A
  pnpm: N/A
Relevant Packages:
  next: 14.0.2-canary.12
  eslint-config-next: N/A
  react: 18.2.0
  react-dom: 18.2.0
  typescript: 5.2.2
Next.js Config:
  output: N/A
```


### Which area(s) are affected? (Select all that apply)

App Router

### Additional context

I see that this issue only occurs when using the app router and it happened because webpack.js sometimes doesn't finish its execution until the test access the function __webpack_require__.n. 

I am not sure if this is a Nextjs issue or Cypress issue, but it works with the same version using the page router, therefore I am opening this issue.