Repository: next.js
Issue: `rewrites` setting does not work with `--experimental-test-proxy` in Pages Router
Labels: bug

### Link to the code that reproduces this issue

https://github.com/hrsh7th/next-testmode-rewrite-repro

### To Reproduce

1. npm ci
2. npm run dev-repro
3. open http://localhost:3000/pages
4. open http://localhost:3000/app (it seems to already fixed in `next@canary`)

### Current vs. Expected behavior

If we use `rewrites` settings in next.config.js and use `--experimental-test-proxy`, Next.js does not handle rewrited requests correctly in `Pages Router`.

I expected to work as the same as without `--exprimental-test-proxy`.

### Verify canary release

- [X] I verified that the issue exists in the latest Next.js canary release

### Provide environment information

```bash
Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 21.6.0: Mon Apr 24 21:11:28 PDT 2023; root:xnu-8020.240.18.701.5~1/RELEASE_ARM64_T8110
Binaries:
  Node: 20.5.1
  npm: 9.8.0
  Yarn: 1.22.21
  pnpm: 8.11.0
Relevant Packages:
  next: 14.0.4-canary.25
  eslint-config-next: 14.0.3
  react: 18.2.0
  react-dom: 18.2.0
  typescript: 5.3.2
Next.js Config:
  output: N/A
```


### Which area(s) are affected? (Select all that apply)

Not sure

### Additional context

The error message is here.

```
Error: No test info
at handleFetch (/path/to/next-testmode-rewrite-repro/node_modules/next/dist/experimental/testmode/server.js:97:15)
at testFetch (/path/to/next-testmode-rewrite-repro/node_modules/next/dist/experimental/testmode/server.js:134:16)
at eval (webpack-internal:///./src/pages/pages/index.page.tsx:37:32)
at query (/path/to/next-testmode-rewrite-repro/node_modules/suspend-react/index.cjs.js:55:27)
at suspend (/path/to/next-testmode-rewrite-repro/node_modules/suspend-react/index.cjs.js:72:39)
at Pokemon (webpack-internal:///./src/pages/pages/index.page.tsx:36:75)
at renderWithHooks (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:5658:16)
at renderIndeterminateComponent (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:5731:15)
at renderElement (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:5946:7)
at renderNodeDestructiveImpl (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:6104:11)
at renderNodeDestructive (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:6076:14)
at renderNode (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:6259:12)
at renderSuspenseBoundary (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:5591:5)
at renderElement (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:5994:11)
at renderNodeDestructiveImpl (/path/to/next-testmode-rewrite-repro/node_modules/react-dom/cjs/react-dom-server.browser.development.js:6104:11)
```

Next.js can contain `app` / `pages` both at the same time so I thought it should be worked in Pages Router too.

But if it doens't matter to fix, feel free to close this.