Putin knows that going nuclear will be the end of his life and his country. I do not think he is that irrational. Putin will be hated in Russia for generations anyway. If he fails spectacularly in Ukraine, he is probably a dead man, so he has to keep up the fight. He is a cornered rat, and may feel he has little to lose.
The original plan was to rapidly occupy heavily Russian regions in the three eastern Ukraine territories and Crimea.
If Ukraine counter attacked, large numbers of ethnic Russian civilians would be killed or displaced, which would have extinguished much of the sympathy for Ukraine in the USA and NATO countries.
Instead, Biden publicly revealed Putin's plan before the War started and boisterously warned Putin not to do it.
Putin took the bait, decided to make a show of force, and ordered a Russian army to attack on a straight line at Kiev, the capital of Ukraine.
Nothing but bad news for Putin ever since.
If Putin had stuck to the original plan, he could have stuck to the original narrative of Russian soldiers protecting ethnic Russians from Ukraine nationalists.
Instead, Putin and Zelensky decided on a real war, at least 100,000 people are dead, and it will cost $1 trillion to rebuild Ukraine.