Add Dockerfiles and compose quickstart

backend/Dockerfile

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+# syntax=docker/dockerfile:1
+
+FROM python:3.12-slim AS base
+
+ENV PYTHONDONTWRITEBYTECODE=1 \
+    PYTHONUNBUFFERED=1
+
+WORKDIR /app
+
+# System deps (keep minimal)
+RUN apt-get update \
+  && apt-get install -y --no-install-recommends curl ca-certificates \
+  && rm -rf /var/lib/apt/lists/*
+
+# Install uv (https://github.com/astral-sh/uv)
+RUN curl -LsSf https://astral.sh/uv/install.sh | sh
+ENV PATH="/root/.local/bin:${PATH}"
+
+# --- deps layer ---
+FROM base AS deps
+
+# Copy only dependency metadata first for better build caching
+COPY pyproject.toml uv.lock ./
+
+# Create venv and sync deps (including runtime)
+RUN uv sync --frozen --no-dev
+
+# --- runtime ---
+FROM base AS runtime
+
+# Copy virtual environment from deps stage
+COPY --from=deps /app/.venv /app/.venv
+ENV PATH="/app/.venv/bin:${PATH}"
+
+# Copy app source
+COPY alembic ./alembic
+COPY alembic.ini ./alembic.ini
+COPY app ./app
+
+# Default API port
+EXPOSE 8000
+
+# Run the API
+CMD ["uvicorn", "app.main:app", "--host", "0.0.0.0", "--port", "8000"]