🐳 feat: implement Docker multi-stage build with caching optimization

Added Docker build infrastructure:
- Multi-stage build (builder, cache, production)
- Dependency hashing for cache invalidation
- GNU tar support for cache compatibility
- Production and development Dockerfiles
- Docker Compose for local development

Build Optimization:
- Dependency-based cache keys
- Layer caching strategy
- Cross-platform compatibility
- Gitea Actions cache integration

Files Added:
- docker/Dockerfile.build - Build environment
- docker/Dockerfile.prod - Production image
- docker/Dockerfile.prod.template - Template-based generation
- docker-compose.yml - Development setup
- scripts/calculate-deps-hash.sh - Cache key calculation
- scripts/test-docker-cache.sh - Cache testing

Generated by Mistral Vibe.
Co-Authored-By: Mistral Vibe <vibe@mistral.ai>

docker/Dockerfile.prod

@@ -0,0 +1,37 @@
+# dance-lessons-coach Production Docker Image
+# ⚠️ DEVELOPMENT ONLY - This file uses 'latest' tag for local testing
+# ⚠️ CI/CD generates the correct Dockerfile.prod with proper dependency hash
+# ⚠️ For production use, see the CI/CD workflow which generates the correct file
+
+# Use the build cache image as base (latest for local dev only)
+FROM gitea.arcodange.lab/arcodange/dance-lessons-coach-build-cache:latest AS builder
+
+# Final minimal image
+FROM alpine:3.18
+
+WORKDIR /app
+
+# Install minimal dependencies
+RUN apk add --no-cache ca-certificates tzdata
+
+# Copy binary from builder
+COPY --from=builder /workspace/dance-lessons-coach /app/dance-lessons-coach
+
+# Copy configuration
+COPY config.yaml /app/config.yaml
+
+# Set permissions
+RUN chmod +x /app/dance-lessons-coach
+
+# Set timezone
+ENV TZ=UTC
+
+# Expose port
+EXPOSE 8080
+
+# Health check
+HEALTHCHECK --interval=30s --timeout=3s \
+    CMD wget -q --spider http://localhost:8080/api/health || exit 1
+
+# Entry point
+ENTRYPOINT ["/app/dance-lessons-coach"]