Add JavaScript SDK public mock integration tests

[wenbinf]

The SDK's default tests mock HTTP transports, so they cannot detect problems reaching the deployed mock API. Add an opt-in suite that sends real requests through both the Node/Axios and Workers/fetch clients.

• Add yarn test-integration, with 12 shared cases per client covering search, podcast/playlist reads, all five playlist writes, response headers, and HTTP 404 handling.
• Restrict requests to the public mock API, send no API key, disable redirects, and enforce request timeouts. Close timers and Miniflare connections after tests.
• Keep default tests offline and run live integration checks in a separate Node.js 24 CI workflow.
• Document local execution and the mock's limitations: fixed responses verify routing and response handling, not persistence or production authorization.

Validation: all 24 live integration tests passed against listen-api-test.listennotes.com; all 84 offline Node/Workers tests, lint, immutable dependency installation, and generated-file checks passed. No new dependencies or SDK runtime changes.