vercel deploy --prebuilt causes system environment variables to disappear

Verify canary release

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

Provide environment information

Operating System:
      Platform: darwin
      Arch: arm64
      Version: Darwin Kernel Version 22.2.0: Fri Nov 11 02:03:51 PST 2022; root:xnu-8792.61.2~4/RELEASE_ARM64_T6000
    Binaries:
      Node: 20.4.0
      npm: 9.7.2
      Yarn: 1.22.19
      pnpm: 8.6.0
    Relevant Packages:
      next: 13.4.17-canary.0
      eslint-config-next: 13.4.16
      react: 18.2.0
      react-dom: 18.2.0
      typescript: 5.1.6
    Next.js Config:
      output: N/A

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

No response

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

https://github.com/Justinfan827/testing-vercel-cli

To Reproduce

compare the deployed site when running:

vercel build
vercel deploy --prebuilt

vercel deploy

Describe the Bug

When running vercel deploy, the environment variable NEXT_PUBLIC_VERCEL_URL is populated correctly. However, when running vercel build and vercel deploy --prebuilt, this env var disappears.

Expected Behavior

NEXT_PUBLIC_VERCEL_URL should always get populated even if running vercel build and vercel deploy --prebuilt

Which browser are you using? (if relevant)