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/Dockerfile

@@ -17,10 +17,16 @@ WORKDIR /app
 COPY package*.json ./
 RUN npm ci --omit=dev && npm cache clean --force
 
-# Copy compiled output from builder
+# Copy compiled output and New Relic preload from builder
 COPY --from=builder /app/dist ./dist
+COPY --from=builder /app/newrelic-preload.js ./newrelic-preload.js
+
+# New Relic agent — configured entirely via environment variables
+ENV NEW_RELIC_NO_CONFIG_FILE=true
+ENV NEW_RELIC_DISTRIBUTED_TRACING_ENABLED=true
+ENV NEW_RELIC_LOG=stdout
 
 EXPOSE 3000
 
-# Run the compiled JS directly — no ts-node, no watch, no devDeps
-CMD ["node", "dist/main"]
+# Preload the New Relic agent (activates only when NEW_RELIC_ENABLED=true)
+CMD ["node", "-r", "./newrelic-preload.js", "dist/main"]