Styles are not removed when navigating away from a page, app router

### Link to the code that reproduces this issue https://github.com/Specy/next-style-bug ### To Reproduce 1. Start the dev server 2. Go to `localhost:3000` (the button is red, the button has a default green background and it was overridden by a local style module in the page) 3. Click the link at the bottom of the page to visit the `/layer` page (here the button has the default green color) 4. Click the link at the bottom of the page to go back to the root page 5. Now the button is green (the style from button of the `/layer` page overrides the one in the main page) https://github.com/Specy/next-style-bug/assets/59029985/466936c5-650b-417d-9cee-2e0236905df5 ### Current vs. Expected behavior Current: The style of the button gets overridden by the styles of `/layer` page Expected: The styles of the `/layer` do not override the ones in the main page ### Verify canary release - [X] I verified that the issue exists in the latest Next.js canary release ### Provide environment information ```bash Operating System: Platform: win32 Arch: x64 Version: Windows 10 Home Binaries: Node: 20.2.0 npm: N/A Yarn: N/A pnpm: N/A Relevant Packages: next: 13.5.4-canary.11 eslint-config-next: 13.5.4 react: 18.2.0 react-dom: 18.2.0 typescript: 5.2.2 Next.js Config: output: N/A ``` ### Which area(s) are affected? (Select all that apply) App Router ### Additional context _No response_