refactor: rebuild NestJS example from scratch with v11 and strict TypeScript
Scaffolded from `nest new --strict` (NestJS v11), stripped CLI boilerplate,
and configured max-strict tsconfig (noUncheckedIndexedAccess, noUnusedLocals,
noUnusedParameters, noImplicitReturns, noImplicitOverride, etc.).
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>