Empty URL search params are swallowed when rewriting via middleware on Vercel

Link to the code that reproduces this issue

https://github.com/migueloller/vercel-middleware-search-params-bug-repro

To Reproduce

Deploy the application to Vercel. The easiest way is using the Vercel CLI. I have a deployed version that can be used to test here.

Visit the path /?foo= and then visit /?foo=bar. Note that while the search params are there for /?foo=bar, they are not there for /?foo=.

Current vs. Expected behavior

The expectation is that URL search params are there even if the value is an empty string. Note, this is only happening because of the rewrite in the middleware. If the middleware.ts file is deleted, then the expected behavior occurs.

Provide environment information

Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 23.6.0: Mon Jul 29 21:13:04 PDT 2024; root:xnu-10063.141.2~1/RELEASE_ARM64_T6020
  Available memory (MB): 16384
  Available CPU cores: 10
Binaries:
  Node: 18.19.0
  npm: 10.2.3
  Yarn: 1.22.21
  pnpm: 8.15.6
Relevant Packages:
  next: 15.0.3 // There is a newer version (15.0.4) available, upgrade recommended! 
  eslint-config-next: 15.0.3
  react: 19.0.0-rc-66855b96-20241106
  react-dom: 19.0.0-rc-66855b96-20241106
  typescript: 5.7.2
Next.js Config:
  output: N/A
 ⚠ There is a newer version (15.0.4) available, upgrade recommended! 
   Please try the latest canary version (`npm install next@canary`) to confirm the issue still exists before creating a new issue.
   Read more - https://nextjs.org/docs/messages/opening-an-issue

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

Middleware

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

Vercel (Deployed)

Additional context

The issue only happens when deploying to Vercel, it does not reproduce during local development. This is likely due to differences in the runtime middleware runs on in Vercel vs local dev.

Start with the linked reproduction and its middleware.ts, deploy it to Vercel with the Vercel CLI, and compare /?foo= with /?foo=bar. Trace the deployed middleware rewrite path in Next.js and add a regression test for preserving an empty search-parameter value; done when the deployed behavior matches local behavior and both URLs are covered.