doc: index: redesign landing page with persona-based navigation

Completely overhaul the documentation landing page to improve user
experience and navigability.

Key changes:
- Replace the static grid list with a modern, responsive HTML/CSS layout.
- Introduce "Persona" cards (App Developer, Hardware Engineer, Product
  Maker) to guide users to relevant sections faster.
- Highlight key reference resources (API, Kconfig, DeviceTree, ...) in a
  dedicated reference section.
- Call out "How to contribute" with a dedicated card.

Signed-off-by: Benjamin Cabé <[email protected]>

Author: kartben