test: add comprehensive test suite with 89% coverage

- Add tests for all backend modules: config, database, models, services,
  routes, middleware, and providers
- Separate dev dependencies using dependency-groups
- Update CLAUDE.md with test commands and project structure
- Add .coverage and .pytest_cache to gitignore

88 tests covering:
- Authentication and authorization
- Model routing and key selection
- Async logging with batch processing
- All API endpoints (chat, openai, anthropic, health)
- LiteLLM wrapper (mocked external calls)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -10,8 +10,23 @@ zzrouter is an AI model API proxy service with OpenAI-compatible and Anthropic s
 
 ```
 zzrouter/
-├── backend/     # Python FastAPI proxy server
-└── frontend/    # (placeholder)
+├── backend/           # Python FastAPI proxy server
+│   ├── app/           # Application code
+│   │   ├── middleware/    # Request/response middleware
+│   │   ├── models/        # Database models
+│   │   ├── providers/     # AI provider clients (OpenAI, Anthropic)
+│   │   ├── routes/        # API route handlers
+│   │   ├── services/      # Business logic
+│   │   ├── config.py      # Configuration settings
+│   │   ├── database.py    # Database setup and utilities
+│   │   └── main.py        # FastAPI app entry point
+│   ├── data/           # SQLite database files
+│   ├── tests/          # Test files
+│   ├── main.py         # Server entry point
+│   └── pyproject.toml  # Python dependencies
+├── frontend/          # Frontend (superpowers skill files only)
+├── docs/              # Documentation
+└── .playwright/       # Playwright browser automation
 ```
 
 ## Backend Commands
@@ -19,13 +34,25 @@ zzrouter/
 ```bash
 cd backend
 
-# Install dependencies
+# Install dependencies (production only)
 uv sync
 
-# Run development server
+# Install dependencies (with dev tools)
+uv sync --group dev
+
+# Run development server (with auto-reload)
 uv run uvicorn app.main:app --reload --port 8000
 
-# Run directly
+# Run production server
+uv run uvicorn app.main:app --port 8000
+
+# Run tests
+uv run pytest -v
+
+# Run tests with coverage
+uv run pytest -v --cov=app --cov-report=term-missing
+
+# Alternative: run directly
 uv run python main.py
 ```