Type-check the TypeScript README quickstart in CI

[kriptoburak]

Goal

Keep the TypeScript README quickstart compatible with the released SDK.

Scope

• Add a minimal compile-only example under examples/.
• Mirror the README's first client-construction workflow.
• Type-check it in the existing test command.
• Do not send a network request.
• Do not require an API key.

Acceptance Criteria

• The example passes strict TypeScript checks.
• The repository's ./scripts/test command passes.
• README snippets and the example use the same public API.
• The example remains deterministic and offline.
• Keep generated SDK files and public contracts unchanged.

Starting Points

• README
• Examples directory
• Contribution guide

This task should fit within 1 working day. It supports newcomer onboarding and OpenSSF evidence.