Update App Proxy API handlers to use Repository

## Goal

Replace DB session usage with Repository calls in API handlers

## Files to Modify

- `src/ai/backend/appproxy/coordinator/api/worker_v1.py`
- `src/ai/backend/appproxy/coordinator/api/worker_v2.py`
- `src/ai/backend/appproxy/coordinator/api/circuit_v1.py`
- `src/ai/backend/appproxy/coordinator/api/circuit_v2.py`
- `src/ai/backend/appproxy/coordinator/api/endpoint.py`
- `src/ai/backend/appproxy/coordinator/api/slot_v1.py`
- `src/ai/backend/appproxy/coordinator/api/slot_v2.py`
- `src/ai/backend/appproxy/coordinator/api/proxy.py`
- `src/ai/backend/appproxy/coordinator/api/health.py`

## Change Pattern

```python
# Before
async with root_ctx.db.begin_readonly_session() as sess:
worker = await Worker.get(sess, worker_id)

# After
worker = await root_ctx.worker_repository.get(worker_id)
```

JIRA Issue: BA-3224

Start by reading the nine listed API handler modules, beginning with worker_v1.py and worker_v2.py, and compare their DB-session accesses with the repository change pattern in the issue. Update every named file so its handlers use the appropriate root_ctx repository calls, then verify that no listed handler still uses the old session-based access pattern.

Written by the indexing model from the issue text.