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: Ubuntu 20.04.0 LTS Sun Jan 15 2023 18:53:52 GMT+0200 (Eastern European Standard Time)
Binaries:
Node: 16.14.2
npm: 7.17.0
Yarn: 1.22.19
pnpm: 7.13.6
Relevant packages:
next: 13.1.3-canary.0
eslint-config-next: N/A
react: 18.2.0
react-dom: 18.2.0

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

App directory (appDir: true)

Link to the code that reproduces this issue

https://stackblitz.com/edit/vercel-next-js-wzcg3h?file=app/about/page.tsx

To Reproduce

1. Go here: https://stackblitz.com/edit/vercel-next-js-wzcg3h?file=app%2Fabout%2Fpage.tsx
2. npm run build (the sandbox starts by default in dev mode, that doesn't work, don't know why)
3. npm run start
4. Click on "Go to About Page"
5. See the logs:
   

Describe the Bug

The client components from the root layout are unmounted and mounted again when you navigate through Links.
In the following sandbox, I created two pages HomePage + AboutPage.

There you will see a root layout having the TestComponent in it.
In the test component, I made an effect where I logged mount and unmount triggers.

This issue is reproducible in build mode.
This issue can also be reproducible in dev mode if the reactStrictMode is true (default).
(I posted on this thread some time ago: #42164 (comment))

Expected Behavior

The client components from the Rootlayout should not unmount on link navigation.

Which browser are you using? (if relevant)

Chrome

How are you deploying your application? (if relevant)

No response