fix(infra): resolve NestJS dist build and Prometheus target issues

NestJS: disable incremental in 6 services tsconfig.json to fix dist
not emitted when nest-cli deleteOutDir conflicts with tsc tsbuildinfo.
classes/iam: import HealthModule in AppModule to fix /healthz 404.
classes: rewrite HealthController to Drizzle getDb from TypeORM DI.
teacher-bff: add /metrics endpoint for Prometheus scraping.
infra: add node/mysql/redis exporters to observability profile.
mysql-exporter v0.15.1 uses command-line flags not DATA_SOURCE_NAME.
prometheus: enable web.enable-lifecycle for hot reload.

services/teacher-bff/src/main.ts

@@ -3,6 +3,7 @@ import { NestFactory } from "@nestjs/core";
 import { AppModule } from "./app.module.js";
 import { env } from "./config/env.js";
 import { initTracer, shutdownTracer } from "./shared/observability/tracer.js";
+import { metricsRegistry } from "./shared/observability/metrics.js";
 
 async function bootstrap(): Promise<void> {
   initTracer();
@@ -12,6 +13,12 @@ async function bootstrap(): Promise<void> {
 
   app.enableShutdownHooks();
 
+  // Prometheus 指标端点：不鉴权，供 Prometheus 抓取。
+  app.getHttpAdapter().get("/metrics", async (_req, res) => {
+    res.set("Content-Type", metricsRegistry.contentType);
+    res.end(await metricsRegistry.metrics());
+  });
+
   await app.listen(env.PORT);
   console.log(`Teacher BFF started on port ${env.PORT}`);
 

services/teacher-bff/src/shared/observability/metrics.ts

@@ -0,0 +1,26 @@
+import promClient from "prom-client";
+
+const registry = new promClient.Registry();
+registry.setDefaultLabels({ service: "teacher-bff" });
+
+registry.registerMetric(
+  new promClient.Counter({
+    name: "teacher_bff_requests_total",
+    help: "Total number of teacher-bff requests",
+    labelNames: ["method", "endpoint", "status"],
+  }),
+);
+
+registry.registerMetric(
+  new promClient.Histogram({
+    name: "teacher_bff_request_duration_seconds",
+    help: "Teacher-bff request duration in seconds",
+    labelNames: ["method", "endpoint"],
+    buckets: [0.01, 0.05, 0.1, 0.3, 0.5, 1, 3, 5],
+  }),
+);
+
+// 自动收集 Node.js 进程级指标（CPU/内存/事件循环/GC等）
+promClient.collectDefaultMetrics({ register: registry });
+
+export { registry as metricsRegistry };