Redirects not working correctly together with middleware

Link to the code that reproduces this issue

https://github.com/serGlazkov/next-redirect-middleware-bug

To Reproduce

• Set up redirects in the next.config.js file.
• Confirm that the redirects are working as expected.
• Add a middleware.ts file to the project.
• Click a link that should trigger a redirect.

Current vs. Expected behavior

Actual Result
The user is redirected to the page, but it's rendered without any properties.

Expected Result
The user should be redirected to the intended page with all the expected properties. (Should work the same as without middleware)

Verify canary release

• I verified that the issue exists in the latest Next.js canary release

Provide environment information

Operating System:
  Platform: darwin
  Arch: x64
  Version: Darwin Kernel Version 22.6.0: Wed Jul  5 22:21:56 PDT 2023; root:xnu-8796.141.3~6/RELEASE_X86_64
Binaries:
  Node: 18.14.2
  npm: 9.5.0
  Yarn: 1.22.19
  pnpm: N/A
Relevant Packages:
  next: 13.5.3
  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)

Middleware / Edge (API routes, runtime), Routing (next/router, next/navigation, next/link)

Additional context

No response

Start with the linked reproduction repository, then compare the redirect behavior with and without middleware.ts using the redirects configured in next.config.js. Verify that the redirected page receives and renders all expected properties, matching behavior when middleware is absent.