test(forward): run Batch E2E outside idle windows

[moonyue-w]

Summary

Set ignore_idle_window: true in the Forward Batch E2E creation request so the scenario can run outside the account's idle window. Preserve all existing completion, task/output, assistant-reply and cleanup assertions.

Why

The Batch E2E previously queued work behind the idle-window policy and could exhaust its 180-second deadline before execution began. This matches the existing Go/Python E2E requests and the TypeScript Batch example.

Verification

• npm run build (included in npm test)
• npm run typecheck
• npm test
• npm run docs:check
• Relevant examples run or import successfully
• Account-backed integration tests run, or not required

Commands and results:

npm test
3,505 tests passed; 0 failures; 0 skips. Includes build, type tests and offline Batch replay.

node --test --test-concurrency=1 --test-name-pattern='^Forward live batch_e2e$' tests/live/forward-live.test.mjs
CN: 1 passed; 0 failures; 0 skips; 6.8 seconds.
Global: 1 passed; 0 failures; 0 skips; 15.5 seconds.
Both runs used the modified repository scenario directly and completed resource cleanup.

Separate full typecheck, documentation generation and example runs were not repeated for this one-line integration-test request change.

Impact

• Public API or behavior changed
• User-facing changes added to CHANGELOG.md under Unreleased, or not applicable (explain below)
• CommonJS, ESM, and subpath exports remain valid
• Generated API documentation updated
• Contract or wire-field fixtures updated
• Go and Python parity considered
• Migration notes added for a breaking change
• No credentials, .env.live, logs, or generated test output committed

Only the Batch E2E request changes. Public SDK defaults, declarations, exports and contracts remain unchanged, so no changelog, generated documentation, fixture update or migration note is needed. Package/export checks are included in npm test.