feat(health): 被动式健康检查 API（FastAPI，覆盖服务健康+数据健康）

在同步进程内内置 FastAPI/uvicorn HTTP endpoint (GET /health)，返回结构化
健康快照，便于运维/监控被动探活：

- 服务健康：cycle_lag（核心指标，超过 3×poll_interval 判 unhealthy）、
  队列状态（pending/error/dead/cleaned 实时查）、capture 累计（enqueued/
  deferred/aged_out）、最近 cycle 时间/耗时/错误。
- 数据健康：解析最近一次定时 compare_ids 报告（不跑全量 compare 太重）、
  实时查 SyncLogArchive 异常痕迹（AgedOut/降级）、SyncQueue dead 行样本。

status 三态：healthy(200) / degraded(503, 有dead/error/aged_out/compare
不一致) / unhealthy(503, 主循环停滞)。状态码映射便于按码告警。

线程模型：uvicorn 占主线程，capture/apply/cleanup 循环跑后台 daemon 线程，
NSSM 停服务时主线程退出、daemon 自动终止。health.enabled=false 时退化为
旧行为（同步循环占主线程）。Web 层(routes/)与业务逻辑(HealthChecker)
解耦，后期加运维接口（compare触发/死信管理/metrics）零结构改动。

零 SQL/零 schema 改动。新增依赖 fastapi/uvicorn[standard]。

src/sync/web/deps.py

@@ -0,0 +1,42 @@
+"""Shared FastAPI dependencies.
+
+The :class:`ServiceState` and :class:`SyncConfig` are created once in
+``service.run`` and injected into routes via ``Depends``, avoiding global
+singletons. Routes get a ready-to-use :class:`HealthChecker` rather than the
+raw state, so each endpoint declares only what it needs.
+"""
+from __future__ import annotations
+
+from fastapi import Depends
+
+from ..config import SyncConfig
+from ..health import HealthChecker, ServiceState
+
+# Bound at app creation time (create_app). Module-level holders are acceptable
+# here because there is exactly one app per process and they are write-once.
+_state: ServiceState | None = None
+_cfg: SyncConfig | None = None
+
+
+def bind(state: ServiceState, cfg: SyncConfig) -> None:
+    """Stash the singletons for the lifetime of this app (called once)."""
+    global _state, _cfg
+    _state = state
+    _cfg = cfg
+
+
+def get_state() -> ServiceState:
+    assert _state is not None, "ServiceState not bound -- call bind() first"
+    return _state
+
+
+def get_config() -> SyncConfig:
+    assert _cfg is not None, "SyncConfig not bound -- call bind() first"
+    return _cfg
+
+
+def get_checker(
+    state: ServiceState = Depends(get_state),
+    cfg: SyncConfig = Depends(get_config),
+) -> HealthChecker:
+    return HealthChecker(state, cfg)