Variables defined in `.env` files that do not begin with `NEXT_PUBLIC_` are not available in Middleware deployed to Vercel

Link to the code that reproduces this issue

https://codesandbox.io/p/devbox/flamboyant-cray-pwlc82

To Reproduce

1. next dev
2. observe that the middleware logs value as defined in .env
3. Deploy to Vercel
4. observe that the middleware logs undefined instead of the value defined in .env

Current vs. Expected behavior

Current

Variables defined in .env files that do not begin with NEXT_PUBLIC_ are not available in Middleware deployed to Vercel.

BUT, all variables defined in Vercel are available in Middleware. This inconsistency is very confusing.

.env files offer more functionality, e.g. MY_PATH="https://${VERCEL_URL}/some/path", so it would be great if it just worked.

I have tried this workaround: https://github.com/vercel/next.js/discussions/39705#discussioncomment-4621291 but it extremely limited since some dependencies access variables using other syntax like process.env[name].

Expected

Consistent behaviour. If all environment variables defined in Vercel are made available to middleware, so too should all environment variables defined in .env files.

Provide environment information

Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 20.6.0: Tue Feb 22 21:10:42 PST 2022; root:xnu-7195.141.26~1/RELEASE_ARM64_T8101
  Available memory (MB): 8192
  Available CPU cores: 8
Binaries:
  Node: 20.10.0
  npm: 10.2.3
  Yarn: N/A
  pnpm: 8.15.4
Relevant Packages:
  next: 14.2.4 // Latest available version is detected (14.2.4).
  eslint-config-next: 14.2.4
  react: 18.3.1
  react-dom: 18.3.1
  typescript: 5.5.2
Next.js Config:
  output: N/A

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

Developer Experience, Middleware, Runtime, Webpack

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

Vercel (Deployed)

Additional context

This issue is related to Vercel deployment, see the discussion here https://github.com/vercel/next.js/discussions/39705

Start with the linked CodeSandbox reproduction and run the documented next dev steps, then deploy it to Vercel and compare the middleware logs for .env variables and Vercel-defined variables. Done means non-NEXT_PUBLIC_ variables behave consistently in Middleware in both environments, including variables referenced through process.env[name].