(I don't think any of us has a definitive answer to that, but that is the question the CIA should be asking)
Even if Putin does order a nuclear strike it’s hard to see how a launch order from Putin would actually lead to a missile getting launched. A lot can happen in the chain of command.. including say a “technical fault” in the missile itself which prevents its launch. Putin may be terminally ill and suicidal but I don’t think anyone other than him is willing to partake in mass suicide.