ci(docs): add a Markdown link checker so docs links don't rot #55

Background

The README, CONTRIBUTING.md, docs/, and the new ADRs link heavily to files and issues. A moved or renamed file silently breaks those links and there's nothing to catch it.

The task

Add a link-checking step to CI over the repo's Markdown so dead relative links fail the build.

• Use an off-the-shelf action (e.g. lycheeverse/lychee-action) or a small script — your call, keep it simple.
• Focus on internal/relative links and anchors first. External URLs are optional (they're flaky and can rate-limit); if you include them, make external failures non-blocking.
• Pin any third-party action to a commit SHA with a trailing # vX comment — see the note at the top of .github/workflows/ci.yml.

Acceptance criteria

• CI fails when a .md file links to a path that doesn't exist.
• The check is green on dev today — fix any broken links you find as part of the PR.

Why this is a good first issue

Pure tooling/docs, no product code. Touches CI lightly and immediately pays off given how link-heavy our docs are.