Feat: Add production-grade multi-stage container image for API

Two-stage build (uv builder + python:3.12-slim runtime) with non-root
user (UID 1001), no dev deps, layer-cache-optimised dep install, and
graceful SIGTERM shutdown. Verified by api/tests/build/verify_production_image.sh
covering build, health endpoint, non-root, stdout logging, secret-free
layers, missing-env-var exit, and dep-layer cache hit. All 102 integration
tests still pass; shellcheck clean.

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

api/Dockerfile.prod

@@ -0,0 +1,51 @@
+# syntax=docker/dockerfile:1
+
+# ════════════════════════════════════════════════
+# Build stage: install production deps via uv
+# ════════════════════════════════════════════════
+FROM ghcr.io/astral-sh/uv:python3.12-bookworm-slim AS builder
+
+WORKDIR /app
+
+ENV UV_COMPILE_BYTECODE=1 \
+    UV_LINK_MODE=copy \
+    UV_PYTHON_DOWNLOADS=never
+
+# Layer cache split: deps only (changes rarely)
+COPY pyproject.toml uv.lock ./
+RUN --mount=type=cache,target=/root/.cache/uv \
+    uv sync --frozen --no-dev --no-install-project
+
+# Layer cache split: source (changes often)
+COPY app/ ./app/
+
+# ════════════════════════════════════════════════
+# Runtime stage: lean image with venv + source
+# ════════════════════════════════════════════════
+FROM python:3.12-slim
+
+WORKDIR /app
+
+RUN apt-get update \
+    && apt-get install -y --no-install-recommends curl \
+    && rm -rf /var/lib/apt/lists/*
+
+RUN groupadd --system --gid 1001 appgroup \
+    && useradd --system --uid 1001 --gid 1001 --no-create-home appuser
+
+COPY --from=builder --chown=appuser:appgroup /app/.venv /app/.venv
+COPY --chown=appuser:appgroup app/ ./app/
+
+USER appuser
+
+ENV PATH="/app/.venv/bin:$PATH"
+
+EXPOSE 8000
+
+HEALTHCHECK --interval=30s --timeout=5s --start-period=10s --retries=3 \
+    CMD curl -f http://localhost:8000/api/v1/health || exit 1
+
+CMD ["uvicorn", "app.main:app", \
+     "--host", "0.0.0.0", \
+     "--port", "8000", \
+     "--timeout-graceful-shutdown", "30"]