We let the world revolve around Russia when we sleep-walked into dependence on Russian oil and gas.
True, and we're currently making the same mistake with China, our dependence on cheap mass-produced items has transformed their economy over the last few decades enabling them to have one of the most advanced military capabilities in the world.
On the original question of whether Putin will use nuclear weapons, there's no doubt that he's willing to use them if he doesn't get what he wants - or at least, can no longer convince the average Russian that he always gets what he wants.
Putin considers himself essential to Russia. Without Putin in charge, there's no point in Russia existing. Without Russia existing, there's no point in the world existing. In his view, there is nothing to lose in destroying the planet in a nuclear war. If he's not a strong, successful leader who can do what he likes, there's no need for anyone or anything to exist.
That's why the MAD strategy doesn't work with him. Ironic, that MAD doesn't work when there is a madman in charge. To work, MAD assumes a basic human desire not to destroy the world or your own people.
We should remember that not all nuclear weapons are world-ending though. "Tactical" nuclear weapons are more on a scale of a Hiroshima-type bomb. Highly destructive and can kill hundreds of thousands, but not world-destroying.
I think that the real risk is Putin deploying a tactical weapon - maybe in Ukraine, maybe in western Europe, or even just in the North Sea - and waiting to see what the response is. If NATO replies with nuclear weapons of its own, Russia can just destroy the planet and be done with it. If NATO doesn't respond, Putin will be emboldened and probably deploy more nuclear weapons until he either gets a response or decides he's captured enough territory.
There are ways out of this situation, but all rely on Putin being removed from power. There is a growing awareness in Russia that perhaps all is not as rosy as their media tell them, but most Russians still believe what they are being told - NATO and the West generally are bulling Russia and threatening their existence.