It is extremely likely that Putin does not think about nuclear weapons the way that you do. If you're not a national security professional then they were almost certainly an infrequent thought before this war. If they did come up you probably considered their use in Europe (or anywhere else) a near impossibility. They were the second-strike option of last resort. If you thought about them at all it was mostly as inescapable Cold War relics held by rational powers or as a desirable insurance policy for every rogue state looking to lock in its survival. Either way, their use was essentially inconceivable.
Putin, on the other hand, has a vast array of nuclear capabilities and nuclear escalation paths that fall far short of MAD. And, not coincidentally at all, he knows (and has stated publicly) that the alliance has a significant advantage over Russia on the conventional warfare front. NATO can run the table in a war with Russia without so much as a thought about first use but Putin would never initiate a war in Europe, even one limited to Ukraine, without seriously considering scenarios where he might elect to do just that or where he might be forced to fall back on the weapons as a last resort.
Putin is also a man driven by an incessantly growing list of grievances ranging from the petty and personal to the geo-political. He has repeatedly aired these grievances both directly to his opponents and publicly. Time and time again he has signaled his intent to seek revenge (or act against a perceived threat) and time and time again he has followed through on those promises. Countries have been invaded, civilian centers and hospitals have been bombed, radioactive materials and nerve agents have been used to carry out assassinations, journalists have been murdered, and god only knows what we don't know.
Putin has also made very clear statements about his willingness to use all weapons at his disposal (explicitly nuclear) to protect Russia from existential threats. When considering this we shouldn't overlook the fact that he sees himself as inseparable from the state. And (very importantly) he gets to personally define what constitutes an existential threat or an act of war against Russia. The surprisingly unified and well-executed surge to assist Ukraine with its defense and the overwhelming economic measures taken to weaken and isolate Russia have likely put us very close to several of Putin's red lines. Standing up to Putin's aggression is essential but in doing so the alliance has to weigh and balance a dizzying array of bad options - even before non-starters like a no-fly zone get thrown in the mix.
I do not believe that Putin is irrational or that he is eager to see this conflict escalate to the unthinkable. He understands the implications of limited first use and he is in no hurry to go there. However, he is immoral and that is nearly as dangerous. There is also increasingly little to constrain him in an environment where he is failing on all fronts, nearing North Korean levels of isolation, and where the off-ramps (don't even mention golden bridges) are seemingly non-existent. One only has to accept so much defeat and humiliation while sitting on a stockpile of thousands of nuclear weapons. We should not lose sight of that fact. If he feels like he needs to use the nuclear option (or the chemical one, for that matter) he will do so.
Balancing all of this will only get more difficult with each passing day but if history is any indication, Putin will send more signals. Some will be discernible in the increasingly indiscriminate and brutal applications of conventional power and some may appear as explicit warnings that he intends to do the unthinkable. If those clear statements of intent come we should take him, finally, at his word. What do we then do with those warnings or, god forbid, a sudden Russian tactical nuclear strike? I don't think we know. There are absolutely no good options.
What do you think? Let me know.