The article goes into NO detail whatsoever: "lonely individuals have a different response to celebrities", "their perception of reality differs from the social norm", but doesn't describe how different. It says that the participants were tasked, among other things, to rate how close they felt to celebrities, but the article doesn't mention the results, not even a single "rate themselves much less close than others"
Off to read the paper when I get the time - https://www.nature.com/articles/s44271-024-00088-3