## Context
- FastAPI app at `src/my_deepagent/api/app.py` needs a lightweight liveness/readiness probe.
- Response shape: `{"status": "ok", "db": <bool>}`; `db` reflects a fast `SELECT 1` round-trip.
- Must degrade gracefully: DB failure returns `db: false`, not a 500.

## Phases
- Locate existing DB session/engine helper used elsewhere in the app.
- Confirm sync vs async session pattern to match endpoint signature.
- Add `ping_db()` helper running `SELECT 1` with short timeout.
- Wrap helper in try/except; return `False` on any DB exception.
- Register `GET /healthz` route on the FastAPI app instance.
- Endpoint calls `ping_db()` and returns the JSON payload.
- Keep endpoint unauthenticated and excluded from rate limits.
- Add response model or `dict[str, Any]` annotation for clarity.

## Verification
- Unit test: mock DB success, assert `{"status": "ok", "db": true}` and 200.
- Unit test: mock DB raising, assert `{"status": "ok", "db": false}` and 200.
- Manual: `curl /healthz` with DB up, then with DB stopped.
- Static checks: `ruff`, `mypy`/`pyright`, `pytest` all pass.
- Confirm no new warnings and CHANGELOG `[Unreleased]` updated.