Combining `basePath`, `rewrites`, and middleware breaks page transitions

Verify canary release

[X] I verified that the issue exists in the latest Next.js canary release

Provide environment information

$ npx --no-install next info

    Operating System:
      Platform: darwin
      Arch: arm64
      Version: Darwin Kernel Version 21.6.0: Mon Aug 22 20:19:52 PDT 2022; root:xnu-8020.140.49~2/RELEASE_ARM64_T6000
    Binaries:
      Node: 19.8.1
      npm: 8.11.0
      Yarn: 1.22.19
      pnpm: 7.1.7
    Relevant packages:
      next: 13.4.4-canary.1
      eslint-config-next: N/A
      react: 18.2.0
      react-dom: 18.2.0
      typescript: 5.0.4

Which area(s) of Next.js are affected? (leave empty if unsure)

Data fetching (gS(S)P, getInitialProps), Middleware / Edge (API routes, runtime), Routing (next/router, next/navigation, next/link)

Link to the code that reproduces this issue or a replay of the bug

https://codesandbox.io/s/github/mizdra/reproduction-nextjs-middleware-basepath-rewrites

https://github.com/mizdra/reproduction-nextjs-middleware-basepath-rewrites

To Reproduce

Start the development server with npm i && npm run dev.
Access http://localhost:3000/base in your browser
Click on the link /1234 (Runtime error occurs)

https://github.com/vercel/next.js/assets/9639995/e0b934b5-fdbc-490d-b7a5-79fd09cb7522

Describe the Bug

When transitioning from page A to page B with the Link component, there is a bug that causes the page component of page A to be rendered using pageProps derived from getServerSideProps of page B. This can result in runtime errors.

This only seems to happen when cleverly combining basePath, rewrites and Middleware (see the reproduction repository for details). The following changes to the Reproduction Repository will prevent the problem.

Remove basePath from next.config.js.
Remove rewrites from next.config.js.
Delete middleware.ts.
Return NextResponse.next() instead of NextResponse.rewrite(req.nextUrl) from middleware.ts

In addition, the problem is reproduced when the length of the path to be transitioned to is less than 4, but not when it is greater than 5. For example, the problem reproduces for transitions to /1234, but not for /12345.

Expected Behavior

When transitioning from page A to page B with a Link component, the page component of page B should be rendered using pageProps derived from getServerSideProps of page B.

Which browser are you using? (if relevant)

Chrome 112.0.5615.137（Official Build）（arm64）

How are you deploying your application? (if relevant)

next dev

vercel / next.js