chore: validate published examples

[varin-nair-factory]

Summary

• Include docs and examples in the published package files list
• Run ESLint over examples with example-specific console/type-assertion allowances
• Make example typechecking use the project defaults and remove the placeholder setup test

Validation

• npm run typecheck
• npm run typecheck:examples
• npm run format:check
• npm test
• npm run lint
• npm run build

Split out from #26.