TypeScript SDK: refactor shared logic between NodeCoordinator and ExecutableCoordinator

[jason810496]

Background

NodeCoordinator duplicates logic that also exists in ExecutableCoordinator, such as metadata validation and schema-version parsing. Extracting the shared parts was agreed as a separate PR during review.

What needs to happen

1. Refactor metadata validation, schema-version parsing, and other shared logic between NodeCoordinator and ExecutableCoordinator into common utilities.

Acceptance criteria

• Shared coordinator logic lives in one place; both coordinators consume it with no duplicated implementations.

Context

• Review thread: Add NodeCoordinator #68548 (comment), deferred in Add NodeCoordinator #68548 (comment)