🐳 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>

scripts/test-docker-cache.sh

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+#!/bin/bash
+# Test Docker build cache functionality locally
+# Usage: scripts/test-docker-cache.sh
+
+set -e
+
+echo "🧪 Testing Docker Build Cache"
+echo "============================"
+echo ""
+
+# Check requirements
+if ! command -v docker >/dev/null 2>&1; then
+    echo "❌ Docker not found. Please install Docker first."
+    exit 1
+fi
+
+if ! command -v go >/dev/null 2>&1; then
+    echo "❌ Go not found. Please install Go 1.26.1+."
+    exit 1
+fi
+
+echo "✅ Requirements met"
+echo ""
+
+# 1. Calculate dependency hash (same as CI)
+echo "1. Calculating dependency hash..."
+# Use shasum on macOS, sha256sum on Linux
+if command -v sha256sum >/dev/null 2>&1; then
+    DEPS_HASH=$(sha256sum go.mod go.sum | sha256sum | cut -d' ' -f1 | head -c 12)
+else
+    DEPS_HASH=$(shasum -a 256 go.mod go.sum | shasum -a 256 | cut -d' ' -f1 | head -c 12)
+fi
+echo "   Dependency hash: $DEPS_HASH"
+echo ""
+
+# 2. Build Docker cache image
+echo "2. Building Docker cache image..."
+IMAGE_NAME="dance-lessons-coach-build-cache:$DEPS_HASH"
+echo "   Image name: $IMAGE_NAME"
+
+docker build -t "$IMAGE_NAME" -f Dockerfile.build .
+echo "✅ Docker image built successfully"
+echo ""
+
+# 3. Test running commands in Docker
+echo "3. Testing Docker execution..."
+
+echo "   Testing 'go version'..."
+docker run --rm -v "$(pwd):/workspace" -w /workspace "$IMAGE_NAME" go version
+echo "   ✅ Go version command works"
+
+echo "   Testing 'go build'..."
+docker run --rm -v "$(pwd):/workspace" -w /workspace "$IMAGE_NAME" go build -o /tmp/test ./cmd/greet
+echo "   ✅ Go build command works"
+
+echo "   Testing 'swag' availability..."
+docker run --rm -v "$(pwd):/workspace" -w /workspace "$IMAGE_NAME" swag --version || echo "   ⚠️  Swag not available"
+echo ""
+
+# 4. Performance comparison
+echo "4. Performance comparison..."
+
+echo "   Running 'go build' natively..."
+START=$(date +%s%N)
+go build -o /tmp/native-test ./cmd/greet > /dev/null 2>&1
+NATIVE_TIME=$((($(date +%s%N) - $START)/1000000))
+echo "   Native build: ${NATIVE_TIME}ms"
+
+echo "   Running 'go build' in Docker..."
+START=$(date +%s%N)
+docker run --rm -v "$(pwd):/workspace" -w /workspace "$IMAGE_NAME" go build -o /tmp/docker-test ./cmd/greet > /dev/null 2>&1
+DOCKER_TIME=$((($(date +%s%N) - $START)/1000000))
+echo "   Docker build: ${DOCKER_TIME}ms"
+
+echo "   Overhead: $((DOCKER_TIME - NATIVE_TIME))ms"
+echo ""
+
+# Clean up
+rm -f /tmp/native-test /tmp/docker-test
+
+echo "✅ Docker cache testing complete!"
+echo ""
+echo "💡 The Docker image is ready for CI use."
+echo "💡 Push this image to your registry for CI caching:"
+echo "   docker tag $IMAGE_NAME your-registry/$IMAGE_NAME"
+echo "   docker push your-registry/$IMAGE_NAME"