When Putin announced that he was putting his nuclear forces on high alert back in February or March, it was not to threaten Ukraine, but to threaten NATO countries who might come to its assistance. I have not since then heard him threaten Ukraine with his nukes. Perhaps I missed his threats? Do you have a link to one?
As for whose fault is what — honestly, would you care, if either Russia launches nukes or NATO does so preemptively, and then the other side inevitably retaliates, and our world dies in flames — would you really care whose fault it would have been? Would it really matter to you?