Middleware: Response headers gets set on Request aswell

Link to the code that reproduces this issue

https://github.com/sommeeeer/opennext-middleware-request-headers-issue

To Reproduce

1. pnpm build && pnpm start
2. curl http://localhost:3000/test
3. Visit http://localhost:3000/issue-page and http://localhost:3000/issue-action

Current vs. Expected behavior

When you set response headers in middleware.ts I expect it not to be on both the request headers and response headers in any route. Can confirm this is an issue on 15.x.x, and on latest 14.

Provide environment information

Operating System:
  Platform: linux
  Arch: x64
  Version: #47~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Wed Oct  2 16:16:55 UTC 2
  Available memory (MB): 14800
  Available CPU cores: 16
Binaries:
  Node: 20.18.0
  npm: 11.1.0
  Yarn: N/A
  pnpm: 9.15.4
Relevant Packages:
  next: 15.2.4 // Latest available version is detected (15.2.4).
  eslint-config-next: 15.2.4
  react: 19.1.0
  react-dom: 19.1.0
  typescript: 5.8.2
Next.js Config:
  output: N/A

Which area(s) are affected? (Select all that apply)

Middleware, Headers

Which stage(s) are affected? (Select all that apply)

next start (local), next dev (local)

Additional context

I tested with standalone build too. Same problem there.

Start with the linked reproduction repository and run pnpm build && pnpm start, then request /test and visit /issue-page and /issue-action. Inspect middleware.ts and the middleware request/response handling involved in those routes; done means response headers set by middleware no longer appear in request headers across the reported local stages.