Add production Dockerfiles and nginx config

Backend: installs non-editable, runs uvicorn without reload.
Frontend: multi-stage build, serves static files via nginx with
API proxy to the backend service and SPA fallback routing.

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

backend/Dockerfile.prod

@@ -0,0 +1,19 @@
+# Production Dockerfile for the backend API
+FROM python:3.14-slim
+
+WORKDIR /app
+
+# Install system dependencies
+RUN apt-get update && apt-get install -y --no-install-recommends \
+    curl \
+    && rm -rf /var/lib/apt/lists/*
+
+# Install Python dependencies
+COPY pyproject.toml README.md alembic.ini ./
+COPY src/ ./src/
+
+RUN pip install --no-cache-dir .
+
+EXPOSE 8000
+
+CMD ["uvicorn", "app.main:app", "--host", "0.0.0.0", "--port", "8000", "--app-dir", "src"]