active_jobs has some stale job information which maybe done

### 🚀 Feature Description and Motivation

1. no job id or name..
2. lots of jobs are checked/refreshed within 1s.

This is probably the reason job can not be scheduled.

```
2026-08-12 05:53:14,568 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,569 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,570 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,571 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,572 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,573 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,574 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,575 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,576 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,577 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
2026-08-12 05:53:14,578 - batch_manager.py:593 - job_updated_handler - WARNING - {"old_category": "_in_progress_jobs", "new_category": "_done_jobs", "event": "Job is not in old category, ignore updating", "logger": "aibrix.batch.batch_manager", "level": "warning", "timestamp": "2026-08-12 05:53:14 UTC"}
^C
```

### Use Case

observability/job scheduling

### Proposed Solution

_No response_

Start in batch_manager.py around line 593 and trace job_updated_handler, then inspect how active_jobs is refreshed and how jobs move between _in_progress_jobs and _done_jobs. Reproduce the repeated warnings if possible and determine how stale job state or rapid refreshes prevent scheduling. Done should include corrected job tracking and evidence that the warning storm and scheduling issue no longer occur.

Written by the indexing model from the issue text.