Add production infrastructure: compiled builds, clustering, connection pooling

Root cause of 502 errors under 30 concurrent users: the production server
was running dev-mode infrastructure (Vite dev server, NestJS --watch,
no DB connection pooling, single Node.js process).

Changes:
- backend/Dockerfile: multi-stage prod build (compiled JS, no devDeps)
- frontend/Dockerfile: multi-stage prod build (static assets served by nginx)
- frontend/nginx.conf: SPA routing config for frontend container
- docker-compose.prod.yml: production overlay with tuned Postgres, memory
  limits, health checks, restart policies
- nginx/production.conf: keepalive upstreams, proxy buffering, rate limiting
- backend/src/main.ts: Node.js clustering (1 worker per CPU, up to 4),
  conditional request logging, production CORS
- backend/src/app.module.ts: TypeORM connection pool (max 30, min 5)
- docs/DEPLOYMENT.md: new Production Deployment section

Deploy with: docker compose -f docker-compose.yml -f docker-compose.prod.yml up -d --build

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

frontend/nginx.conf

@@ -0,0 +1,20 @@
+# Minimal nginx config for serving the React SPA inside the frontend container.
+# The outer nginx reverse proxy forwards non-API requests here.
+
+server {
+    listen 80;
+    server_name _;
+    root /usr/share/nginx/html;
+    index index.html;
+
+    # Serve static assets with long cache (Vite hashes filenames)
+    location /assets/ {
+        expires 1y;
+        add_header Cache-Control "public, immutable";
+    }
+
+    # SPA fallback — any non-file route returns index.html
+    location / {
+        try_files $uri $uri/ /index.html;
+    }
+}