🐳 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

@@ -0,0 +1,57 @@
+# dance-lessons-coach Docker Image
+# Multi-stage build for production deployment
+
+# Stage 1: Build binary
+FROM golang:1.26.1-alpine AS builder
+
+WORKDIR /app
+
+# Copy go mod files
+COPY go.mod go.sum ./
+RUN go mod download
+
+# Copy source code
+COPY . ./
+
+# Install swag and generate Swagger docs only if they don't exist
+RUN if [ ! -f pkg/server/docs/swagger.json ]; then \
+    echo "📝 Generating Swagger documentation..." && \
+    go install github.com/swaggo/swag/cmd/swag@latest && \
+    cd pkg/server && go generate && \
+    echo "✅ Swagger documentation generated"; \
+    else \
+    echo "✅ Swagger documentation already exists, skipping swag installation and generation"; \
+    fi
+
+# Build binary
+RUN CGO_ENABLED=0 GOOS=linux go build -o /dance-lessons-coach ./cmd/server
+
+# Stage 2: Final image
+FROM alpine:3.18
+
+WORKDIR /app
+
+# Install dependencies
+RUN apk add --no-cache ca-certificates tzdata
+
+# Copy binary from builder
+COPY --from=builder /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"]