feat(infra): add OTel auto-instrumentations across all services

NestJS 6 services use getNodeAutoInstrumentations().

Python 2 services use FastAPIInstrumentor. Go 2 services use otelgin.

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

@@ -0,0 +1,27 @@
+import { getNodeAutoInstrumentations } from "@opentelemetry/auto-instrumentations-node";
+import { OTLPTraceExporter } from "@opentelemetry/exporter-trace-otlp-http";
+import { NodeSDK } from "@opentelemetry/sdk-node";
+import { env } from "../../config/env.js";
+
+let sdk: NodeSDK | null = null;
+
+export function initTracer(): void {
+  if (!env.OTEL_EXPORTER_OTLP_ENDPOINT) return;
+
+  sdk = new NodeSDK({
+    serviceName: "teacher-bff",
+    traceExporter: new OTLPTraceExporter({
+      url: `${env.OTEL_EXPORTER_OTLP_ENDPOINT}/v1/traces`,
+    }),
+    instrumentations: [getNodeAutoInstrumentations()],
+  });
+
+  sdk.start();
+  console.log("Tracer initialized with auto-instrumentations");
+}
+
+export async function shutdownTracer(): Promise<void> {
+  if (sdk) {
+    await sdk.shutdown();
+  }
+}