feat(api): vertical slice POST /v1/agent/chat and the Celery ping path

One request exercises every layer: JWT auth, quota reservation, a versioned
prompt through the LLM gateway, a cost row, quota commit or refund, and the
unified envelope. The trivial ping task proves the queue routing and the
tk_task transitions before any real long-running task is written.

Routes are mounted at the /api/v1 base path of 架构文档 §9.1; /v1/* is
rewritten to it at the ASGI layer so both spellings work from one route table.

apps/api/routers/health.py

@@ -0,0 +1,59 @@
+"""Liveness, readiness and metrics. Mounted at the root, outside ``/api/v1``.
+
+``/healthz`` must never touch a dependency: if it did, a slow database would
+make the orchestrator kill healthy processes. ``/readyz`` is the one that checks
+dependencies, because a process that cannot reach PostgreSQL should be taken out
+of the load-balancer rotation but not restarted.
+"""
+
+from __future__ import annotations
+
+from fastapi import APIRouter, Response
+from prometheus_client import CONTENT_TYPE_LATEST, generate_latest
+from sqlalchemy import text
+
+from packages.shared.config import get_settings
+from packages.shared.db import get_session_factory
+from packages.shared.errors import AppError, ErrorCode
+from packages.shared.logging import get_logger
+from packages.shared.observability import REGISTRY
+from packages.shared.redis_client import get_redis
+from packages.shared.response import ok
+
+router = APIRouter(tags=["ops"])
+logger = get_logger(__name__)
+
+
+@router.get("/healthz", summary="Liveness probe")
+async def healthz() -> dict[str, object]:
+    settings = get_settings()
+    return ok({"status": "ok", "app": settings.app_name, "env": settings.app_env})
+
+
+@router.get("/readyz", summary="Readiness probe (checks PostgreSQL and Redis)")
+async def readyz() -> dict[str, object]:
+    checks: dict[str, str] = {}
+
+    try:
+        factory = get_session_factory()
+        async with factory() as session:
+            await session.execute(text("SELECT 1"))
+        checks["postgres"] = "ok"
+    except Exception as exc:
+        checks["postgres"] = f"error: {type(exc).__name__}"
+
+    try:
+        await get_redis().ping()
+        checks["redis"] = "ok"
+    except Exception as exc:
+        checks["redis"] = f"error: {type(exc).__name__}"
+
+    if any(v != "ok" for v in checks.values()):
+        logger.warning("readiness_failed", checks=checks)
+        raise AppError(ErrorCode.UPSTREAM_ERROR, message="依赖未就绪", data={"checks": checks})
+    return ok({"status": "ready", "checks": checks})
+
+
+@router.get("/metrics", summary="Prometheus scrape endpoint", include_in_schema=False)
+async def metrics() -> Response:
+    return Response(content=generate_latest(REGISTRY), media_type=CONTENT_TYPE_LATEST)