Write an async batch processor over an API with concurrency limits, retries with jitter, and error isolation.

Use bounded async workers behind a queue or semaphore, batch when supported, apply exponential backoff with jitter only to retryable failures, honor Retry-After, isolate per-item errors, and checkpoint idempotent progress.

Test empty input, one-element input, duplicates, boundary indices, invalid states, and the largest allowed size; state time and space complexity.