Does the emotional, illicit online relationship that the questioner engaged in constitute a violation of his covenant with Allah not to commit Zina (fornication/adultery) which necessitates a Hudd (prescribed punishment), and is an expiation due from him?

A mere promise is not an oath, but it must be fulfilled, and failure to fulfill it is a sign of hypocrisy. Zina (adultery/fornication) is one of the gravest indecencies and has two meanings: a general one that includes everything Allah has forbidden, such as looking or touching, and a specific one that necessitates a prescribed punishment (hadd). The questioner must repent from the mentioned sin, and there is no expiation (kaffarah) due on him.