CLAUDE: Fix Docker build for UV migration

Fixed Docker build issues to complete UV migration.

## Changes

### README.md
- Created backend README.md (required by hatchling build system)
- Simple quick start guide referencing CLAUDE.md

### Dockerfile
- Added `build-essential` for compiling native extensions (pendulum Rust code)
- Updated copy steps to include README.md in both dev and prod stages
- Dockerfile now successfully builds both development and production images

### .dockerignore
- Added exception `!README.md` to allow README.md through
- Keeps other *.md files excluded as intended

## Testing
- ✅ Development image builds successfully (paper-dynasty-backend:dev-uv)
- ✅ Production image builds successfully (paper-dynasty-backend:prod-uv)
- ✅ Container starts and UV installs dependencies correctly
- ✅ Application attempts to start (fails only on missing .env, as expected)

## Build Results
- Dev image: 73 packages installed (with dev deps)
- Prod image: 57 packages installed (no dev deps)
- Both stages use `uv sync --frozen` for reproducible builds
- Build time: ~1-2 minutes per stage

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

backend/.dockerignore

@@ -44,6 +44,7 @@ docker-compose.yml
 
 # Documentation
 *.md
+!README.md
 docs/
 
 # OS

backend/Dockerfile

@@ -14,6 +14,7 @@ ENV PYTHONUNBUFFERED=1 \
 RUN apt-get update && apt-get install -y \
     curl \
     postgresql-client \
+    build-essential \
     && rm -rf /var/lib/apt/lists/*
 
 # Install UV
@@ -25,8 +26,8 @@ WORKDIR /app
 # Development stage
 FROM base as development
 
-# Copy dependency files
-COPY pyproject.toml uv.lock ./
+# Copy dependency files (including README.md referenced in pyproject.toml)
+COPY pyproject.toml uv.lock README.md ./
 
 # Install all dependencies (including dev)
 RUN uv sync --frozen
@@ -43,8 +44,8 @@ CMD ["uv", "run", "python", "-m", "uvicorn", "app.main:socket_app", "--host", "0
 # Production stage
 FROM base as production
 
-# Copy dependency files
-COPY pyproject.toml uv.lock ./
+# Copy dependency files (including README.md referenced in pyproject.toml)
+COPY pyproject.toml uv.lock README.md ./
 
 # Install production dependencies only
 RUN uv sync --frozen --no-dev

backend/README.md

@@ -0,0 +1,20 @@
+# Paper Dynasty Backend
+
+FastAPI-based real-time baseball game engine with WebSocket support.
+
+## Quick Start
+
+```bash
+# Install UV
+curl -LsSf https://astral.sh/uv/install.sh | sh
+
+# Install dependencies
+uv sync
+
+# Run server
+uv run python -m app.main
+```
+
+## Documentation
+
+See `CLAUDE.md` for full documentation.