It has never been likely that any government would simply decide to start a nuclear war. Putin clearly has many delusions, but he knows how MAD works. But there are three nuclear war scenarios that seem plausible.
One is an unintended escalation to a nuclear war that nobody wanted. This has almost happened several times, from the Cuban Missile Crisis to Able Archer 83. It is not impossible that Russian and NATO forces end up shooting at one another (say an aerial incursion, intentional or not, along the Polish-Ukrainian frontier) and this escalates to nukes because each side believes the other is going for it.
Another scenario is that Russia, faced with a quagmire in Ukraine without a clear path to an exit, decides to use a nuclear weapon in a “tactical” context (i.e. to achieve a limited military goal such as destroying the entrenched Ukrainian forces in the east). The possibility of tactical nuclear warfare has been debated since the Korean War, with many strategists believing this would inevitably escalate to a full strategic nuclear exchange (how can anyone know that you plan to stop after just 1-2 nukes?). How would NATO respond if Putin did this in Ukraine, which is not under the NATO nuclear umbrella? How about if he did it in, say, Poland as part of the escalation scenario described above? Again I think Putin understands MAD and that this is not very likely, but in a situation of military desperation (with Russia seeing no path to conventional victory and no way to deescalate without a dangerous loss of face), perhaps it can’t be ruled out.
The third and (in my opinion) scariest scenario is that Putin reaches a position where his political survival (and perhaps his very literal survival—there’s no retirement home for deposed dictators) is at stake and that he feels he has no way out. A combination of military quagmire and economic pain from sanctions could eventually face the regime with a loss of support from elites and masses alike. Putin could conceivably see no non-nuclear way to force an end to international sanctions and support for the Ukrainian resistance, and no way to fold his chips and end the war without making his domestic position even worse (who’s more vulnerable: a despised dictator, or a despised dictator who just made himself look weak?). If this happens, the nuclear blackmail could seriously ratchet up, as Putin could see nuclear blackmail against the West as his only lever for ending the pressure without a self-defeating show of weakness. At that point, would it be possible to deescalate? Would the West see negotiation with a nuclear hostage-taker as an invitation for further nuclear blackmail in the future? If his bluff is called, what would Putin do if he truly believes he has nothing to lose? Would the chain of command carry out his order, especially in a scenario where he may already be losing support from the military? This to me is the darkest scenario because we could no longer assume that all sides want to deescalate from all-out nuclear war.