feat(ci): add build-and-push-api job for ghcr.io/cartsnitch/api

Merges PR #75. QA-approved (Checkout Charlie) and CTO-approved (Savannah Savings). All CI checks pass. Resolves CAR-221, unblocks auth restoration (CAR-200).

Dockerfile

@@ -1,3 +1,5 @@
+# Stage 1: Build dependencies
+# Build context is the repo root.  Paths below are relative to the root.
 FROM python:3.12-slim AS build
 
 RUN apt-get update && apt-get install -y --no-install-recommends \
@@ -6,18 +8,19 @@ RUN apt-get update && apt-get install -y --no-install-recommends \
     && rm -rf /var/lib/apt/lists/*
 
 WORKDIR /app
-COPY pyproject.toml ./
-COPY src/ ./src/
+COPY api/pyproject.toml ./
+COPY api/src/ ./src/
 RUN pip install --no-cache-dir --prefix=/install .
 
+# Stage 2: Production image
 FROM python:3.12-slim AS prod
 
 WORKDIR /app
 RUN adduser --system --group --uid 1000 app
 COPY --from=build /install /usr/local
-COPY src/ ./src/
-COPY alembic.ini ./
-COPY alembic/ ./alembic/
+COPY api/src/ ./src/
+COPY api/alembic.ini ./
+COPY api/alembic/ ./alembic/
 
 USER 1000
 EXPOSE 8000