The statement that the covariant derivative of the metric tensor is identically zero in general relativity is a fundamental identity (known as the metricity condition) that requires no citation.
The claim states a fundamental mathematical fact in differential geometry and general relativity (the compatibility of the Levi-Civita connection with the metric tensor, leading to a vanishing covariant derivative). None of the retrieved papers discuss this standard identity, and as a definitional property of standard Riemannian or pseudo-Riemannian geometry with the metric connection, it qualifies as common knowledge.