🐳 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.build

@@ -0,0 +1,43 @@
+# Build environment Dockerfile with pre-installed Go tools and dependencies
+# Optimized for CI/CD pipeline speed
+# Updated to include Node.js for GitHub Actions compatibility
+
+FROM golang:1.26.1-alpine AS builder
+
+# Install build dependencies
+RUN apk add --no-cache \
+    git \
+    bash \
+    curl \
+    make \
+    gcc \
+    musl-dev \
+    bc \
+    grep \
+    sed \
+    jq \
+    ca-certificates \
+    nodejs \
+    npm \
+    postgresql-client \
+    tar  # Add GNU tar for cache compatibility
+
+# Set up Go environment
+ENV GOPATH=/go
+ENV PATH=$GOPATH/bin:/usr/local/go/bin:/usr/local/bin:/usr/bin:/bin
+WORKDIR /go/src/dance-lessons-coach
+
+# Install common Go tools
+RUN go install github.com/swaggo/swag/cmd/swag@latest && \
+    go install golang.org/x/tools/cmd/goimports@latest && \
+    go install honnef.co/go/tools/cmd/staticcheck@latest
+
+# Copy only go.mod and go.sum first for dependency caching
+COPY go.mod go.sum ./
+RUN go mod download && go mod verify
+
+# Simple build environment - source code is mounted at runtime
+WORKDIR /workspace
+
+# Pre-download common Go tools (already installed in base)
+# RUN go install github.com/swaggo/swag/cmd/swag@latest