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>

changelog/2026-04-12_dockerize.md

@@ -0,0 +1,19 @@
+# 2026-04-12 — Dockerize all containers
+
+**Timestamp:** 2026-04-12T15:00:00
+
+## Summary
+
+Added proper Dockerfiles for backend and frontend. Split compose setup into production (`docker-compose.yml`) and development (`docker-compose.dev.yml`) modes. Updated README to reflect new container architecture.
+
+## Files Added
+
+- `backend/Dockerfile` — multi-stage build: pip install in builder stage, minimal python:3.12-slim runtime; runs uvicorn in production mode
+- `frontend/Dockerfile` — multi-stage build: Node 20 Alpine builds the Vite bundle, nginx:alpine serves the static files
+- `frontend/nginx.conf` — nginx config for SPA fallback routing and `/api/` reverse proxy to the backend container
+- `docker-compose.dev.yml` — development overrides: mounts source for hot reload, uses Vite dev server instead of nginx
+
+## Files Modified
+
+- `docker-compose.yml` — rewritten: proper `build.context` + `dockerfile` references, health check on db, `depends_on` with `condition: service_healthy`, env var interpolation via `${VAR:-default}`, frontend now served on port 80 via nginx
+- `README.md` — updated Current State, added Containers table, replaced install options with Production / Development / Local sections