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>

package.json

@@ -17,13 +17,17 @@
   },
   "devDependencies": {
     "@types/node": "^25.6.0",
-    "vitest": "^4.1.5",
+    "@types/ws": "^8.5.10",
     "@vitest/coverage-v8": "^4.1.5",
     "turbo": "^2.3.0",
-    "typescript": "^5.7.0"
+    "typescript": "^5.7.0",
+    "vitest": "^4.1.5"
   },
   "engines": {
     "node": ">=20.0.0"
   },
-  "packageManager": "pnpm@9.0.0"
+  "packageManager": "pnpm@9.0.0",
+  "dependencies": {
+    "ws": "^8.16.0"
+  }
 }