He won't and probably not. The only way he will order a nuclear strike is if Russia is about to be dissolved or if he is about to be overthrown. Unless Russians financial situation gets a LOT worse, there is no risk of Russia dissolving, as Ukraine is not seeking to invade. Putin will not be overthrown unless he dramatically steps up conscription and starts targeting oligarchs families as conscription possibilities. He knows that to do so would be suicide.
In either scenario, once it has reached that point Putin will have pissed off literally every single person that matters and they would have no reason to listen to him.
Regarding Ukraine not seeking to invade Russia. Almost NOBODY seeks to invade Russia, because Russia has nothing that anyone wants that can't be obtained much more easily and cheaply by simply buying it. Furthermore, were one to invade Russia, you then become responsible for what happens in the epitome of shithole state.
Plus, the more the world bends to that threat, the more every other country will pursue nuclear weapons. Giving too wide a berth to Russia is more dangerous for nuclear proliferation than bowing to their threats.
If Russia were to strike Ukraine with a nuclear bomb, first and foremost that puts every nation on a knife's edge globally... someone else with an itchy trigger finger could launch against Russia in the confusing hours afterwards. Next up, the PRC and India would likely abandoned Russia as waves of condemnation would flood the global media. Finally, the whole goal of the war is to take Ukraine, not to make it uninhabitable... why nuke what you want to own?
Nukes don't have to leave behind radiation and make an area uninhabitable anymore. Those were the "Dirty" fission bombs. Fusion bombs are considered more clean.
Yeah, more clean but not completely... this is not to mention the amount of damage caused by the bomb. Striking Kiev or another city would effectively decimate Ukraine's infrastructure and economy for decades. If the goal of the war is to subjugate, you don't want to be in the hook for all those repairs. A nuke on any of Ukraine's cities would make that dam break last year look like nothing.
FYI the United States has always maintained a first-strike policy as official nuclear doctrine. There is no language restricting nuclear weapons to just nuclear retaliation.
There's a lot of wealthy oligarchs living in luxury who wouldn't want their lifestyles threatened/ended by nuclear war. Similarly, Putins chain of command can't be poor and dumb. They also have comparable luxury and lifestyles, and are smart enough to understand that nuclear war most probably would end everything they have. Putin himself is an umpteen billionaire.
Just sayin', these people that control the nukes have the most to lose if they use 'em.
As much as Putin is self-centered, he does have grandchildren and he probably cares about a legacy, which makes me a little more assured that he won't do something that insane.