Here's the plan in markdown format:

```markdown
## Context
- Existing FastAPI app at `src/my_deepagent/api/app.py`
- Need health check endpoint with DB connectivity test
- DB ping should be quick `SELECT 1` query

## Phases
1. Locate main FastAPI router/instance
2. Add new `/healthz` route handler
3. Implement DB connection check
4. Structure response format
5. Add error handling for DB failures

## Verification
- Manual test with running server
- Unit test for 200/500 responses
- Verify DB ping timeout<100ms
- Check response JSON schema
```