tooling: add real TypeScript typechecking (tsc --noEmit)

[TheStack-ai]

Problem

npm run typecheck currently runs node scripts/build.mjs --check, which performs syntax stripping only via stripTypeScriptTypes. It does not catch semantic type errors like Type 'string' is not assignable to 'number'.

Proposed approach

1. Add typescript as a devDependency.
2. Replace or augment the typecheck script with tsc --noEmit.
3. Wire it into the default test script and (later) CI (infra: set up GitHub Actions CI (build + test on Node 22.x) #2).

The repo already has a strict tsconfig.json (strict, noUncheckedIndexedAccess, exactOptionalPropertyTypes) — just no compiler honoring it yet.

Win-win

• Contributor: a concrete, well-scoped first PR with immediate positive impact.
• Project: catches real regressions before users see them.

Pointers

• scripts/build.mjs — current syntax-only "typecheck"
• tsconfig.json — strict config ready to use
• package.json — scripts.typecheck