TypeScript SDK: Airflow-level integration tests for coordinator-mode tasks

[jason810496]

Background

End-to-end integration coverage for coordinator-mode TypeScript tasks, including the daemon-based execution path, was deferred across the SDK interface and NodeCoordinator PRs. CI coverage was also listed as a next step.

What needs to happen

1. Add Airflow-level integration tests for coordinator-mode TypeScript tasks, including the daemon-based end-to-end path.
2. Wire the coverage into CI.

Acceptance criteria

• A coordinator-mode TypeScript task runs end to end in an integration test executed by CI.

Context

• Add TypeScript task SDK public interface #67908 (PR description)
• Add NodeCoordinator #68548 (PR description)