Verify canary release

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

Provide environment information

Operating System:
      Platform: linux
      Arch: x64
      Version: #1 SMP PREEMPT_DYNAMIC Thu Jun 15 02:15:40 UTC 2023
    Binaries:
      Node: 18.16.0
      npm: 8.11.0
      Yarn: 1.22.19
      pnpm: N/A
    Relevant Packages:
      next: 13.4.8-canary.14
      eslint-config-next: N/A
      react: 18.2.0
      react-dom: 18.2.0
      typescript: 4.9.5
    Next.js Config:
      output: N/A

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

App directory (appDir: true)

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

https://github.com/alvarlagerlof/next-js-draft-mode-repro

To Reproduce

Run the repro in dev or build.

1. Click the link on / to enable draft mode.
2. Go back to /
3. Draft mode is not enabled

Describe the Bug

isEnabled from draftMode() always returns false with export const runtime = "edge"

Expected Behavior

isEnabled returns true after draftMode().enable() is ran,

Which browser are you using? (if relevant)

No response

How are you deploying your application? (if relevant)

Seems to happen locally, in dev, build, and on Vercel

_NEXT-1477