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>

backend/tests/test_routes_health.py

@@ -0,0 +1,16 @@
+"""Tests for health check route."""
+import pytest
+from fastapi.testclient import TestClient
+
+from app.main import app
+
+
+class TestHealthRoute:
+    """Test health check endpoint."""
+
+    def test_health_check(self):
+        """Test health check returns ok."""
+        client = TestClient(app)
+        response = client.get("/health")
+        assert response.status_code == 200
+        assert response.json() == {"status": "ok"}