docs: migrate docs site from Docusaurus to Astro + Starlight

[andrewfulton9]

Summary

• Replaces the Docusaurus docs site with Astro + Starlight, styled with nebari design tokens/components (button, spinner, GitHub link) pulled from the nebari-design system.
• Deploys to Cloudflare Pages via a new Docs GitHub Action (build, unit test, internal link check, deploy), with PR preview URLs and automatic preview cleanup on close, replacing the old GitHub Pages workflow.
• Migrates the existing intro content and updates docs/README.md and .gitignore for the new toolchain (Node >=22, npm).
• Closes [DOC] - Convert docs engine to astro #157.

Ported from the pattern established in nebari-dev/nebi-pack#40, adapted to this repo (no top-level Makefile exists here, so Makefile/root-README changes were dropped in favor of docs/README.md). Also fixes a bug present in that reference: Starlight's customCss loads each file as an independent stylesheet, so the nebari design tokens' @theme block never shared a build with an actual @import "tailwindcss" — components rendered unstyled. Consolidated into one docs/src/styles/tailwind.css entry point.

Test plan

• npm ci && npm test — 10/10 passing (remark-base-links plugin)
• npm run typecheck — 0 errors
• npm run build — succeeds, docs/dist/index.html produced
• bash scripts/check-links.sh — LINKS_OK at both BASE=/ and BASE=/chat-pack/
• npm run preview — visually verified in a headless browser: nebari magenta theme, Geist font, sidebar, and filled GitHub button all render correctly
• Confirm CLOUDFLARE_API_TOKEN/CLOUDFLARE_ACCOUNT_ID secrets and a chat-pack Cloudflare Pages project exist for the new docs.yml/docs-preview-cleanup.yml workflows to deploy successfully