Refactor: Move backend files to backend/ directory and split .gitignore

backend/tests/api/test_api_main.py

@@ -0,0 +1,9 @@
+from fastapi.testclient import TestClient
+from ea_chatbot.api.main import app
+
+client = TestClient(app)
+
+def test_health_check():
+    response = client.get("/health")
+    assert response.status_code == 200
+    assert response.json() == {"status": "ok"}