#1 and #3 may be grammatically correct, but they sound strange. #2 sounds the most natural in my opinion.

1. "They don't have enthusiasm in anything." - nope, but you can say They don't show enthusiasm in anything. But They don't show enthusiasm for anything. is more likely. 2. "They don't have enthusiasm for anything." - yes, a winner. They are not enthusiastic in anything. - could be, "in" like this means sort of while doing. It is less likely to be useful in conversation. but better is They are not enthusiastic for anything. - means .. for doing anything

Your question has to do with preposition collocations. In this case, it's enthusiasm FOR [something] and enthusiastic ABOUT [something]. See https://www.eslbuzz.com/common-preposition-collocations-in-english-2/

xx

Olivia is correct: native speakers, at least in the USA, say "They don't have enthusiasm for anything" or "They are not enthusiastic about anything." You can also say, "They are enthusiastic about nothing." (because if you say "The are not XXX about anything," you can pretty much always say "The are XXX about nothing.")