Switch backend Docker image to Alpine multi-stage

Dockerfile

@@ -1,18 +1,29 @@
-FROM python:3.12-slim
-
-ENV PYTHONDONTWRITEBYTECODE=1 \
-    PYTHONUNBUFFERED=1
+FROM python:3.12-alpine AS builder
 
 WORKDIR /app
 
-# Install runtime dependencies from local package metadata.
+RUN apk add --no-cache build-base libffi-dev openssl-dev cargo
+
 COPY pyproject.toml /app/pyproject.toml
 COPY app /app/app
 COPY scripts /app/scripts
 COPY README.md /app/README.md
 
 RUN pip install --no-cache-dir --upgrade pip && \
-    pip install --no-cache-dir .
+    pip wheel --no-cache-dir --wheel-dir /wheels .
+
+FROM python:3.12-alpine
+
+ENV PYTHONDONTWRITEBYTECODE=1 \
+    PYTHONUNBUFFERED=1
+
+WORKDIR /app
+
+RUN apk add --no-cache libstdc++ libffi openssl
+
+COPY --from=builder /wheels /wheels
+RUN pip install --no-cache-dir --upgrade pip && \
+    pip install --no-cache-dir /wheels/*
 
 EXPOSE 8000