ci(docs): validate internal Starlight links (base-aware)

[NachoVazquez]

Summary

After the Astro Starlight migration (#229) and Diátaxis rewrite (#230), internal docs links use an explicit /lumberjack/ prefix because Astro does not auto-prepend base on markdown/MDX hrefs. That is correct for the GitHub Pages project site (base: '/lumberjack'), but nothing in CI fails if a next-steps target, redirect destination, or reference slug drifts.

Add starlight-links-validator (or equivalent) so broken internal links fail the docs build or a dedicated CI check.

Why

• Markdown links are not base-relative by default; typos and renamed slugs (e.g. /guides/usage → /guides/log-with-the-service) only show up in manual smoke or production.
• TypeDoc reference pages are generated at build time under reference/** (gitignored). Link targets like /lumberjack/reference/core/classes/lumberjackservice/ must resolve against that output.
• Review of docs: Diátaxis rewrite and TypeDoc API reference #230 flagged this as a cheap guardrail so the explicit /lumberjack/ convention stays honest.

Proposed approach

1. Add starlight-links-validator to packages/docs/lumberjack-docs-app (Starlight plugin in astro.config.mjs).
2. Confirm it respects base: '/lumberjack' (absolute same-origin links under the base).
3. Run validation as part of nx build docs-lumberjack-docs-app and/or nx typecheck / a small lint target so CI’s existing nx affected -t lint build e2e catches failures.
4. Optionally exclude external URLs if the plugin is noisy; keep internal + same-site checks strict.

Acceptance criteria

• A deliberately broken internal link in a docs page fails CI (or the docs build) with a clear path + target.
• Valid /lumberjack/... links to Getting Started, Guides, Understanding, What’s New, and generated Reference pages pass.
• No requirement to drop the explicit /lumberjack/ prefix (that stays the correct pattern for this site).
• Documented in a one-liner near the docs app config or project README if setup is non-obvious.

Context

• Site: packages/docs/lumberjack-docs-app
• Related: docs: migrate docs site from docusaurus to astro starlight #229, docs: Diátaxis rewrite and TypeDoc API reference #230
• Production: https://ngworker.github.io/lumberjack/