feat: integrate Datadog APM + Sentry error tracking with CloudWatch metrics FRE-4806

- Add CloudWatch metrics emitter (api_latency, api_requests, api_errors)
- Add request monitoring middleware for API (latency, error rate, throughput)
- Register error-handling, logging, and monitoring middleware in server.ts
- Add Datadog log forwarding via HTTP intake API
- Add application-level CloudWatch alarms for P99 latency, error rate, throughput
- Inject Datadog/Sentry env vars and secrets into ECS task definitions
- Add DD_API_KEY and SENTRY_DSN to ECS secrets
- Create CloudWatch log groups for datadog and sentry services
- Update .env.example with AWS_REGION and monitoring variables
- Add @aws-sdk/client-cloudwatch dependency to monitoring package

Co-Authored-By: Paperclip <noreply@paperclip.ing>

packages/monitoring/tsconfig.json

@@ -0,0 +1,9 @@
+{
+  "extends": "../../tsconfig.base.json",
+  "compilerOptions": {
+    "outDir": "./dist",
+    "rootDir": "./src",
+    "composite": true
+  },
+  "include": ["src"]
+}