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I've never heard anyone in a real leadership position in Russia make much mention of the use of nuclear weapons at all, let alone any 'promises'. It goes without saying that any nuclear armed country reserves the right, and probably has plans to, use nuclear weapons if there is an existential threat. So the non-crazies in Russia are not in the habit of saying it. Of course the Russians have their contingent of crazies in their political classes who will say (and may well do) any damn thing. Unlike in the U.S., these types don't really seem to get a hold of any real levers of power. Yet. Thank God.
On the other hand, you cannot turn around without bumping into someone who 'knows' that Putin is a maniac who is minutes away from pushing the button. And since it is said so often (in the echo chamber) most people believe that they have in fact heard it straight from the horse's mouth too!
Russia seems to have planned to straight-out win in a conventional way any altercation they cannot avoid, and their plans seem very sound so far and it looks like they could handily beat NATO so long as they stick to their game. A lot of the things have gone better than they probably hoped for (foreign relations and trade in particular.) The Collective West is in panic mode for want of decent analysis and planning, and they really don't know whether to shit or go blind at the moment. That (and pretty much that alone) is what is causing a fair amount of risk to the planet at this time.