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_config.py

@@ -0,0 +1,47 @@
+"""Tests for config module."""
+import pytest
+from app.config import DB_PATH, HOST, PORT, LOG_BATCH_SIZE, LOG_FLUSH_INTERVAL, MODEL_PROVIDER_MAP
+
+
+class TestConfig:
+    """Test configuration constants."""
+
+    def test_db_path_is_pathlib_path(self):
+        """Test DB_PATH is a Path object."""
+        from pathlib import Path
+        assert isinstance(DB_PATH, Path)
+
+    def test_db_path_contains_data_dir(self):
+        """Test DB_PATH points to data directory."""
+        assert "data" in str(DB_PATH)
+        assert "zzrouter.db" in str(DB_PATH)
+
+    def test_host_default(self):
+        """Test HOST default value."""
+        assert HOST == "0.0.0.0"
+
+    def test_port_default(self):
+        """Test PORT default value."""
+        assert PORT == 8000
+
+    def test_log_batch_size_positive(self):
+        """Test LOG_BATCH_SIZE is positive."""
+        assert LOG_BATCH_SIZE > 0
+
+    def test_log_flush_interval_positive(self):
+        """Test LOG_FLUSH_INTERVAL is positive."""
+        assert LOG_FLUSH_INTERVAL > 0
+
+    def test_model_provider_map_contains_openai(self):
+        """Test MODEL_PROVIDER_MAP contains OpenAI models."""
+        assert "gpt" in MODEL_PROVIDER_MAP
+        assert "o1" in MODEL_PROVIDER_MAP
+        assert "o3" in MODEL_PROVIDER_MAP
+        assert MODEL_PROVIDER_MAP["gpt"] == "openai"
+        assert MODEL_PROVIDER_MAP["o1"] == "openai"
+        assert MODEL_PROVIDER_MAP["o3"] == "openai"
+
+    def test_model_provider_map_contains_anthropic(self):
+        """Test MODEL_PROVIDER_MAP contains Anthropic models."""
+        assert "claude" in MODEL_PROVIDER_MAP
+        assert MODEL_PROVIDER_MAP["claude"] == "anthropic"