Avoid layout unmount/remount

## 🐛 Bug Report

Most classic D2 sites will use the same layout component on every single page, apart from a few rare exceptions (like a code playground implemented with a custom page).

When navigating from one page to the other, the layout should not unmount/remount unnecessarily.

Currently, when navigating from the home page to the /docs page, the layout unmounts/remounts.

The only case I found where it does not unmount/remount is when navigating from one doc to another.

Avoiding unmounts/remounts when possible is important for 2 reasons:
- faster transition from one page to another
- avoid resetting state of the layout

Probably not urgent to work on this, just wanted to backlog it somewhere :)

Useful link: https://www.gatsbyjs.org/packages/gatsby-plugin-layout/

## To Reproduce

```
yarn docusaurus swizzle @docusaurus/theme-classic Navbar
```

Add this button somewhere in the navbar:

```
const TestButton = () => {
const [bool, setBool] = useState(false);
return (
setBool((b) => !b)}>Toggle me {String(bool)}
);
};
```


## Expected behavior

Navigating should not reset the button state

## Actual Behavior

The button state is reset

---

Edit: this is also a problem for our mobile drawer that may not animate properly on all page transitions, see https://github.com/facebook/docusaurus/discussions/11063#discussioncomment-12763738