Setting Cookies Via Server Action Reloads Entire App

Verify canary release

• 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 22.4.0: Mon Mar  6 20:59:28 PST 2023; root:xnu-8796.101.5~3/RELEASE_ARM64_T6000
    Binaries:
      Node: 16.14.0
      npm: 8.3.1
      Yarn: 1.22.19
      pnpm: 6.11.0
    Relevant packages:
      next: 13.4.4-canary.0
      eslint-config-next: 13.4.3
      react: 18.2.0
      react-dom: 18.2.0
      typescript: 5.0.4

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/johnson-jesse/next-server-action-cookie

To Reproduce

1. Clone repo, install, run dev.
2. Click the first button labeled with "Via Server Action With Cookies"
3. Notice the whole app re-renders.
4. Optionally turn on "Highlight updates when components render." from developer window to see updates from button clicks.

Describe the Bug

Setting cookies in a server action causes the entire app to reload. This appears as a render glitch most noticeable when the layout is using a custom font that also needs to load.

https://github.com/vercel/next.js/assets/10335064/6dd72eca-93e5-460e-ab4f-38d6e9a73dd2

Expected Behavior

Setting cookies in a server action does not cause the entire app to reload thus avoiding loading the font again.

Which browser are you using? (if relevant)

Chrome Version 112.0.5615.137 (Official Build) (x86_64)

How are you deploying your application? (if relevant)

N/A

Start with the linked next-server-action-cookie reproduction and its App Router setup; run it in development and click “Via Server Action With Cookies” while watching component updates. Trace the server action and cookie-setting behavior in the Next.js app directory, then verify that setting the cookie no longer reloads the entire app or causes the custom font to load again.