feat: add production deployment config

- Add docker-compose.prod.yml with env var support
- Add frontend/Dockerfile.prod with nginx for static serving
- Fix Zulip notification to run in thread pool (avoid blocking)
- Use Zulip time format for timezone-aware display
- Add Zulip @mentions for users matched by email

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

docker-compose.prod.yml

@@ -0,0 +1,52 @@
+services:
+  db:
+    image: postgres:16-alpine
+    environment:
+      POSTGRES_USER: ${POSTGRES_USER:-postgres}
+      POSTGRES_PASSWORD: ${POSTGRES_PASSWORD:?POSTGRES_PASSWORD required}
+      POSTGRES_DB: ${POSTGRES_DB:-availability}
+    volumes:
+      - postgres_data:/var/lib/postgresql/data
+    healthcheck:
+      test: ["CMD-SHELL", "pg_isready -U postgres"]
+      interval: 5s
+      timeout: 5s
+      retries: 5
+    restart: unless-stopped
+
+  backend:
+    build:
+      context: ./backend
+      dockerfile: Dockerfile
+    environment:
+      DATABASE_URL: postgresql+asyncpg://${POSTGRES_USER:-postgres}:${POSTGRES_PASSWORD}@db:5432/${POSTGRES_DB:-availability}
+      SYNC_DATABASE_URL: postgresql://${POSTGRES_USER:-postgres}:${POSTGRES_PASSWORD}@db:5432/${POSTGRES_DB:-availability}
+      SMTP_HOST: ${SMTP_HOST:-}
+      SMTP_PORT: ${SMTP_PORT:-587}
+      SMTP_USER: ${SMTP_USER:-}
+      SMTP_PASSWORD: ${SMTP_PASSWORD:-}
+      ZULIP_SITE: ${ZULIP_SITE:-}
+      ZULIP_EMAIL: ${ZULIP_EMAIL:-}
+      ZULIP_API_KEY: ${ZULIP_API_KEY:-}
+      ZULIP_STREAM: ${ZULIP_STREAM:-general}
+    ports:
+      - "8000:8000"
+    depends_on:
+      db:
+        condition: service_healthy
+    restart: unless-stopped
+
+  frontend:
+    build:
+      context: ./frontend
+      dockerfile: Dockerfile.prod
+      args:
+        VITE_API_URL: ${VITE_API_URL:?VITE_API_URL required}
+    ports:
+      - "8080:8080"
+    depends_on:
+      - backend
+    restart: unless-stopped
+
+volumes:
+  postgres_data: