Motivation

• Make the task dead-letter queue (DLQ) durable so failed tasks survive process restarts for debugging and recovery.
• Provide simple HTTP endpoints to inspect, retry, and discard DLQ entries.
• Ensure DLQ writes are atomic to avoid partial/corrupt files.

Description

• Added DLQ persistence to lib/agent-runtime/task-queue.ts including a DeadLetterTaskEntry shape, persistDeadLetterQueue() and loadDeadLetterQueue() helpers, and support for overriding the path via TASK_DLQ_FILE (default /.data/task-dlq.json).
• Persist DLQ on state changes and hydrate the in-memory queue at startup by calling loadDeadLetterQueue(); writes use a temp file + rename for atomic updates.
• Exposed a paginated listing endpoint GET /api/tasks/dead-letter that returns entries and pagination metadata via app/api/tasks/dead-letter/route.ts.
• Implemented POST /api/tasks/dead-letter/[id]/retry to move a DLQ task back to pending and DELETE /api/tasks/dead-letter/[id] to permanently discard an entry via app/api/tasks/dead-letter/[id]/retry/route.ts and app/api/tasks/dead-letter/[id]/route.ts.
• Added listDeadLetterEntries() and discardDeadLetterTask() helpers and wired persistence calls into failTask() and retryDeadLetterTask().
• Extended __tests__/api/tasks.test.ts to set up a temp TASK_DLQ_FILE, verify file persistence/reload, and exercise the new list/retry/delete endpoints.

Testing

• Ran the focused tests for the change with npm test -- __tests__/api/tasks.test.ts, and they passed (6 tests passed).
• Ran npm test which completed but failed unrelated suites due to a missing dependency (lru-cache) in other parts of the repo; this is unrelated to the DLQ changes.
• Ran lint/type checks and npx tsc --noEmit; these surfaced pre-existing unrelated lint/type errors and missing packages (lru-cache, @wagmi/connectors) but did not indicate issues with the DLQ functionality.

Closes #192