In your example, naming a website site “NYT Cooking” and linking to NYT recipes would be misleading to users, a blatant violation of the Times trademark and could be interpreted as unfair competition. I have no intention to mislead users, misuse Times trademarks, or act in a way that is unfair to the Times.
Your point about being non-commercial is well taken. It’s true that JULIA could be commercialized, though it’s not clear how at this point. My main argument is that commercial or not, deep linking from within chatbots should be protected under fair use.