Improve API doc

What does this merge request do and why?

This MR updates the API documentation to reflect the current state of the world.

• Move API documentation to a separate page /docs/api.md
• Add /v1/chat API
• Add /ai alias
• Update /code schema
• Add reference to interactive API docs site

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

Merge request checklist

• Tests added for new functionality. If not, please raise an issue to follow up.
• Documentation added/updated, if needed.