Move documentation website to alexandrite-website

[purefunctor]

Goal

Move the documentation website out of this repository into alexandrite-website for the 0.1.x release.

Scope

• Migrate the documentation website to alexandrite-website.
• Remove the ./docs directory completely from this repository.
• Remove or update documentation-website CI configuration.
• Remove documentation-website setup from .agents/setup.
• Audit related tooling, configuration, agent guidance, and references; remove website-only infrastructure and update links and instructions to point to the new repository.

Ensure the website can be built and deployed from its new repository, and that this repository's remaining CI and development setup no longer depend on ./docs.