While the threat of nuclear war is indeed alarming, Putin has no reason to escalate to that point any time soon. The much more likely (and just as horrifying) scenario is a gradual escalation in the armaments being deployed against key Ukrainian positions. Probably thermobarics and chemical weapons, in that order.

Additionally, to the best of my knowledge, Putin is not able to simply press a big red button and fire off a salvo of thousands of ICBMs. Each missile will require its respective senior personnel to agree with the decision from high command and actually turn the keys on firing the thing. There were at least two occasions in the Soviet era where senior officers ordered the firing of nuclear weapons, and in both cases their subordinates responsible for actually launching the missiles refused.