Ukraine

Yes, he may do that even in a literal sense, or at least destroy what's called the Russian federation.
I doubt the federation will remain whole after this war is over. And if it collapses, Russia will lose even more power than they did when thee Soviet Union collapsed.

my fear is NATO will only wag a finger at them in case they do use a nuke

Yes I have that fear too, many videos and articles have been made about why Putin will not do this. But in the end it all relies on Putin being rational, but if he were rational he would end the war, as that is what a lot of people around him have wanted for a long time. And now even the citizens of Moscow want it too, because Putin can't shield them from the consequences of the war anymore.
If he thinks he cannot afford to lose, and he cannot win either, I could see Putin taking the mad way out. Putin is not the smart guy we were led to believe for many years. In fact it turns out that he is a one trick pony. The trick being projection of power through misdirection. And that trick has stopped working.
So Putin's threats to EU and UK about possible nuclear attacks, are originally merely tricks to spread fear, to prevent allies from helping Ukraine. And it actually worked against Joe Biden, which made him follow a policy where he prevented Ukraine from attacking Russia, because he was afraid of what Putin would do if Russia was losing.

But Russia is clearly losing now, and we can't allow Putin to win because fear of his possible insanity. Because fear is his only trick, and he will use it every opportunity he gets.
If you have read about Putin, you know learned the trick as a child, and practiced its use and refined it when he was in the KGB, and he also used it to win his first Presidential election, where he staged a terrorist attack that he then claimed only he could protect the Russians against.