feat: add production deployment config

- Add docker-compose.prod.yml and Caddyfile for Caddy reverse proxy
- Add production stages to frontend Dockerfile (nginx for static files)
- Fix monorepo package exports for production builds (dist/src paths)
- Add CORS_ORIGIN env var for cross-origin config
- Add Better Auth baseURL, cookie domain, and trusted origins from env
- Use VITE_API_URL for API calls in auth-client and play route
- Add credentials: include for cross-origin fetch requests
- Remove unused users table from schema

docker-compose.prod.yml

@@ -0,0 +1,91 @@
+services:
+  caddy:
+    container_name: lila-caddy
+    image: caddy:2-alpine
+    ports:
+      - "80:80"
+      - "443:443"
+    volumes:
+      - ./Caddyfile:/etc/caddy/Caddyfile
+      - caddy_data:/data
+      - caddy_config:/config
+    restart: unless-stopped
+    depends_on:
+      api:
+        condition: service_healthy
+    networks:
+      - lila-network
+
+  api:
+    container_name: lila-api
+    build:
+      context: .
+      dockerfile: ./apps/api/Dockerfile
+      target: runner
+    env_file:
+      - .env
+    restart: unless-stopped
+    healthcheck:
+      test:
+        ["CMD-SHELL", "wget -qO- http://localhost:3000/api/health || exit 1"]
+      interval: 5s
+      timeout: 3s
+      retries: 5
+    depends_on:
+      database:
+        condition: service_healthy
+    networks:
+      - lila-network
+
+  web:
+    container_name: lila-web
+    build:
+      context: .
+      dockerfile: ./apps/web/Dockerfile
+      target: production
+      args:
+        VITE_API_URL: https://api.lilastudy.com
+    restart: unless-stopped
+    networks:
+      - lila-network
+
+  database:
+    container_name: lila-database
+    image: postgres:18.3-alpine3.23
+    env_file:
+      - .env
+    environment:
+      - PGDATA=/var/lib/postgresql/data
+    volumes:
+      - lila-db:/var/lib/postgresql/data
+    restart: unless-stopped
+    healthcheck:
+      test: ["CMD-SHELL", "pg_isready -U ${POSTGRES_USER} -d ${POSTGRES_DB}"]
+      interval: 5s
+      timeout: 5s
+      retries: 5
+    networks:
+      - lila-network
+
+  forgejo:
+    container_name: lila-forgejo
+    image: codeberg.org/forgejo/forgejo:11
+    volumes:
+      - forgejo-data:/data
+    environment:
+      - USER_UID=1000
+      - USER_GID=1000
+    ports:
+      - "2222:22"
+    restart: unless-stopped
+    networks:
+      - lila-network
+
+networks:
+  lila-network:
+
+volumes:
+  lila-db:
+  caddy_data:
+  caddy_config:
+  forgejo-data: