Dockerize backend, frontend, and database into separate containers

- backend/Dockerfile: multi-stage Python build (builder + slim runtime)
- frontend/Dockerfile: multi-stage Node build + nginx:alpine serving
- frontend/nginx.conf: SPA routing + /api/ reverse proxy to backend
- docker-compose.yml: production compose with health checks and proper dependency ordering
- docker-compose.dev.yml: dev overrides with hot reload via volume mounts

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

docker-compose.dev.yml

@@ -0,0 +1,20 @@
+# Development overrides — hot reload for backend and frontend
+# Usage: docker compose -f docker-compose.yml -f docker-compose.dev.yml up --build
+
+services:
+
+  backend:
+    command: uvicorn app.main:app --host 0.0.0.0 --port 8000 --reload
+    volumes:
+      - ./backend:/app
+
+  frontend:
+    build:
+      context: ./frontend
+      target: builder          # stop at the Node stage, skip nginx
+    command: npm run dev -- --host 0.0.0.0
+    ports:
+      - "5173:5173"
+    volumes:
+      - ./frontend:/app
+      - /app/node_modules