feat: add New Relic APM instrumentation to backend

Add Node.js New Relic agent with an on/off switch via NEW_RELIC_ENABLED
in .env. Uses a preload script (-r newrelic-preload.js) so the agent
loads before all other modules. Configured entirely through environment
variables — no newrelic.js config file needed.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend/package.json

@@ -8,7 +8,7 @@
     "start": "nest start",
     "start:dev": "nest start --watch",
     "start:debug": "nest start --debug --watch",
-    "start:prod": "node dist/main",
+    "start:prod": "node -r ./newrelic-preload.js dist/main",
     "lint": "eslint \"{src,apps,libs,test}/**/*.ts\"",
     "test": "jest",
     "test:watch": "jest --watch",
@@ -37,6 +37,7 @@
     "reflect-metadata": "^0.2.2",
     "rxjs": "^7.8.1",
     "typeorm": "^0.3.20",
+    "newrelic": "latest",
     "uuid": "^9.0.1"
   },
   "devDependencies": {