docs: add documentation style check - #6

Installs the organisation documentation check so the rules in
docs/STYLE_GUIDE.md are enforced instead of relying on review.

• scripts/check_style.py — the checker. Phase 1 blocking rules: leaked
  absolute paths, broken relative links, missing AGENTS.md / CLAUDE.md.
• .github/workflows/docs-check.yml — runs the checker on every pull request.
• AGENTS.md — one sentence under ## Local checks pointing at it.
• .gitignore — keeps check output out of the tree.

Phase 2 rules (naming, language, content boundaries) stay advisory until the
existing files are cleaned up, so this does not turn current pull requests red.

Where the working tree also carries cleanups, they are part of the same commit:

• Committed out/ directories removed from the index and archived outside the
  repository. They carried roughly 100 absolute home paths.
• Absolute home paths in research documents replaced with $PROJECTS_ROOT/ and
  <codex-job-root>/.
• Broken relative links repaired after earlier renames.

Verified: python scripts/check_style.py --phase 1 reports zero blocking
findings, and actionlint accepts the new workflow.