Not a very satisfying answer because it doesn't answer why Capote would slander Vidal in the first place. Indeed the feud existed before the Esquire slander took place so it's incorrect/hallucinatory for Bing Chat to say "The feud began when...".

Oh, and references (2) and (3) seem to be hallucinated and are unrelated to the question and response despite being cited inline. The other ref links are valuable but well then it's just a search engine with more noise.