I’m pretty chill. It’s unlikely that nuclear war will break out, but it could happen. I think it’s still less likely than during the Cold War.
I suspect he's surprised, if not stunned, by the difficulty that his forces are facing. So (while I would prefer he not risk it) I suspect his nukes won't work as expected either. I say that as someone who lives in the Boston suburbs, which I suspect is a high priority target for his subs.
Most importantly, perhaps, is that if it is WW3, it's going to be the world against Russia. Iran may try to help if they feel an obligation; I don't think China will because they're smart enough to see it's a lot cause.
If we assume Putin is mad, there's no reason why he wouldn't throw a nuke. Due to downside being inevitable, WW3 is a logical outcome. Otherwise we are just letting him throw nukes.