Update website to Next.js 13 `app/` directory

[fracek]

We should take advantage of all the new features in next.js 13, like React Server Components.

At the moment, the website uses chakra ui which is not compatible with RSC.

• Switch to shadcn ui while keeping the current color scheme.
• Use RSC for the layout, and client components for navigation and code samples.
• We should investigate using rehype pretty code for code blocks.

[fracek]

This demo from vercel is useful to understand what's new in next 13.

[Laki997]

I will be on it.

[fracek]

This is now done.