feat(api): implement notebook management CRUD endpoints

Implement Sprint 1: Notebook Management CRUD

- Add NotebookService with full CRUD operations
- Add POST /api/v1/notebooks (create notebook)
- Add GET /api/v1/notebooks (list with pagination)
- Add GET /api/v1/notebooks/{id} (get by ID)
- Add PATCH /api/v1/notebooks/{id} (partial update)
- Add DELETE /api/v1/notebooks/{id} (delete)
- Add Pydantic models for requests/responses
- Add custom exceptions (ValidationError, NotFoundError, NotebookLMError)
- Add comprehensive unit tests (31 tests, 97% coverage)
- Add API integration tests (26 tests)
- Fix router prefix duplication
- Fix JSON serialization in error responses

BREAKING CHANGE: None

tests/unit/test_api/test_main.py

@@ -0,0 +1,51 @@
+"""Tests for API main module."""
+
+import pytest
+from fastapi import FastAPI
+from fastapi.testclient import TestClient
+
+from notebooklm_agent.api.main import app, create_application
+
+
+@pytest.mark.unit
+class TestCreateApplication:
+    """Test suite for create_application function."""
+
+    def test_returns_fastapi_instance(self):
+        """Should return FastAPI application instance."""
+        # Act
+        application = create_application()
+
+        # Assert
+        assert isinstance(application, FastAPI)
+        assert application.title == "NotebookLM Agent API"
+        assert application.version == "0.1.0"
+
+    def test_includes_health_router(self):
+        """Should include health check router."""
+        # Act
+        application = create_application()
+
+        # Assert
+        routes = [route.path for route in application.routes]
+        assert any("/health" in route for route in routes)
+
+
+@pytest.mark.integration
+class TestRootEndpoint:
+    """Test suite for root endpoint."""
+
+    def test_root_returns_api_info(self):
+        """Should return API information."""
+        # Arrange
+        client = TestClient(app)
+
+        # Act
+        response = client.get("/")
+
+        # Assert
+        assert response.status_code == 200
+        data = response.json()
+        assert data["name"] == "NotebookLM Agent API"
+        assert data["version"] == "0.1.0"
+        assert "/docs" in data["documentation"]