Run typecheck in CI

[ada33-arch]

Follow-up to #17, which added TypeScript but left nothing in the pipeline checking it — a type error could land on main with CI green.

Rebuilt on current main (4b58087) to resolve a merge conflict; see Conflict resolution below for what changed.

Change

Adds one job to .github/workflows/ci.yml:

typecheck:
  runs-on: ubuntu-latest
  steps:
    - uses: actions/checkout@v4
    - uses: actions/setup-node@v4
      with:
        node-version: '22'
        cache: 'npm'
    - run: npm ci
    - run: npm run typecheck

A separate job rather than a step on lifecycle-demo, so the two run in parallel and a red check points at the TypeScript instead of the Actions demo. npm ci rather than npm install installs exactly what package-lock.json pins and fails if the lockfile has drifted.

Plus two small CLAUDE.md touch-ups that follow from it:

• The ci.yml layout entry now names both jobs, and the Commands section notes that CI runs typecheck on every PR — Refresh CLAUDE.md to match what the repo actually contains #19 was written before this job existed.
• Adds the one gotcha Refresh CLAUDE.md to match what the repo actually contains #19 doesn't cover, and the only one here that has actually broken CI: the root "type": "module" applies to every .js in the repo, including Actions scripts the runner executes directly. That's the entire reason .github/actions/lifecycle-demo/package.json exists — delete it as an apparently redundant two-line manifest and the JS action dies with ReferenceError: require is not defined in ES module scope.

Both edits keep #19's existing bullet style rather than restructuring it.

Conflict resolution

This branch previously carried its own full CLAUDE.md rewrite. #19 landed the same refresh on main while this PR sat in draft, so that commit was dropped rather than merged — it duplicated work that's already on main, and resolving in its favour would have clobbered a merged change. What survived is the typecheck job, which main still doesn't have, plus the two touch-ups above.

On #14 / #15

#14 tried to add Node setup and was reverted after breaking CI — it pasted actions/setup-node boilerplate, every option empty, into .github/actions/docker-demo/action.yml, a Docker action whose runs: block takes an image and args rather than steps. This puts the setup in a workflow job and sets only the two options needed.

Verification

• npm run typecheck exits 0 on this branch.
• The gate isn't vacuous: appending const broken: number = "not a number"; to agent.ts makes it exit 1 with TS2322, back to 0 once reverted.
• main's own documented action recipe still runs verbatim after the rebuild, producing greeting=hello, world!.