[Content Migration] Migrate Documentation to Nuxt Content

### Epic

4867

### Description

## Objective
Migrate the `/docs` section from 11ty to Nuxt. Given the complexity of documentation, we will utilize Nuxt Content's document-driven mode or custom Vue layouts.

## Tasks
- [ ] Recreate the documentation layout, including the sidebar navigation and table of contents, using Vue components.
- [ ] Move 11ty copy_docs.js logic to a Nuxt's git import to `content/docs/` directory.
- [ ] Update code highlighting configurations (migrate to Nuxt Content's Shiki integration).
- [ ] Ensure any interactive Vue components used in our main app can now be embedded directly in the docs markdown.
- [ ] Delete legacy docs from 11ty and remove Nuxt proxy rules for `/docs/**`.

## Acceptance Criteria
- Docs are served by Nuxt.
- Code snippets are highlighted correctly.
- Main app Vue components can be rendered inside the docs markdown.

### Acceptance Criteria

_No response_

### Have you provided an initial effort estimate for this issue?

I have provided an initial effort estimate