Second errata to “Distance covariance in metric spaces”

There is a slight gap and error in Remark 3.4 of Ann. Probab. 41, no. 5 (2013), 3284–3305, that was not noticed before the first errata were published (Ann. Probab. 46, no. 4 (2018), 2400–2405). We take this opportunity to provide some additional updates as well.