Does a wife's relaying to her husband general, non-private conversations of her friends about their life matters, such as their vacation plans, constitute backbiting that falls under the ruling of the noble verse: "Would any of you like to eat the flesh of his brother when dead? You would detest it"?

Carrying tales between people with the intention of causing mischief is backbiting (namimah (definition)). Merely informing the husband about what transpired between the wife and her friends does not fall under backbiting. However, it is not appropriate to inform him of every detail, especially if it leads to harm or if it was a secret. The husband should refrain from asking about matters that do not concern him. The verse mentioned in the question pertains to gheebah (backbiting), which is mentioning a person with what they dislike in their absence, and not namimah (tale-carrying).