feat(server): 可观测性 Phase 1 — 健康检查路由 + Prometheus 指标 + 连接池/事件积压监控

- 添加 /health/live 存活探针别名（原 /health + /health/ready 保留）
- 新增 metrics middleware：http_requests_total 计数器 + http_request_duration_seconds 直方图
- Prometheus exporter 独立端口 9090（可通过 ERP__SERVER__METRICS_PORT 覆盖）
- 后台任务每 30s 采样 DB 连接池活跃/空闲连接数（pg_stat_activity）
- 后台任务每 30s 采样 EventBus pending 事件积压数
- UUID 路径归一化避免高基数（/api/v1/users/:id/posts）

crates/erp-server/src/tasks.rs

@@ -51,3 +51,69 @@ async fn run_cleanup(db: &sea_orm::DatabaseConnection) -> Result<(), sea_orm::Db
 
     Ok(())
 }
+
+/// 启动 DB 连接池 + EventBus 积压指标采样任务。
+///
+/// 每 30 秒采样一次并导出为 Prometheus gauge：
+/// - `db_pool_connections_active` — 当前活跃连接数
+/// - `db_pool_connections_idle` — 当前空闲连接数
+/// - `eventbus_pending_total` — pending 状态的领域事件数
+pub fn start_pool_metrics(db: sea_orm::DatabaseConnection) {
+    tokio::spawn(async move {
+        let mut interval = tokio::time::interval(Duration::from_secs(30));
+        loop {
+            interval.tick().await;
+            sample_pool_metrics(&db).await;
+            sample_eventbus_backlog(&db).await;
+        }
+    });
+    tracing::info!("DB 连接池 + EventBus 积压指标采样已启动（每 30 秒采样一次）");
+}
+
+async fn sample_pool_metrics(db: &sea_orm::DatabaseConnection) {
+    use sea_orm::FromQueryResult;
+
+    #[derive(FromQueryResult)]
+    struct CountRow {
+        cnt: i64,
+    }
+
+    // 通过 pg_stat_activity 查询当前连接数
+    let stmt = sea_orm::Statement::from_string(
+        sea_orm::DatabaseBackend::Postgres,
+        "SELECT COUNT(*)::bigint AS cnt FROM pg_stat_activity WHERE state = 'active'".to_string(),
+    );
+    if let Ok(Some(row)) = CountRow::find_by_statement(stmt).one(db).await {
+        metrics::gauge!("db_pool_connections_active").set(row.cnt as f64);
+    }
+
+    let stmt = sea_orm::Statement::from_string(
+        sea_orm::DatabaseBackend::Postgres,
+        "SELECT COUNT(*)::bigint AS cnt FROM pg_stat_activity WHERE state = 'idle'".to_string(),
+    );
+    if let Ok(Some(row)) = CountRow::find_by_statement(stmt).one(db).await {
+        metrics::gauge!("db_pool_connections_idle").set(row.cnt as f64);
+    }
+}
+
+async fn sample_eventbus_backlog(db: &sea_orm::DatabaseConnection) {
+    use sea_orm::FromQueryResult;
+
+    #[derive(FromQueryResult)]
+    struct CountRow {
+        cnt: i64,
+    }
+
+    let stmt = sea_orm::Statement::from_string(
+        sea_orm::DatabaseBackend::Postgres,
+        "SELECT COUNT(*)::bigint AS cnt FROM domain_events WHERE status = 'pending'".to_string(),
+    );
+    match CountRow::find_by_statement(stmt).one(db).await {
+        Ok(Some(row)) => {
+            metrics::gauge!("eventbus_pending_total").set(row.cnt as f64);
+        }
+        _ => {
+            tracing::debug!("EventBus 积压采样：无法获取 pending 事件数");
+        }
+    }
+}