The current situation is very serious, but fundamentally both sides are aware of the severity and more aware of the state of the opposite side (primarily via better intelligence).
That seems to be more of a threat to the Russian leadership than the Cuban missiles were to the American leadership. I imagine the "should we do it? should we press the button?" conversations are a lot more serious in Russia.
On board they also had a higher ranking officer which overruled it. That was a close call.
I'd work on the assumption that something like that will happen or has already happened and it isn't public knowledge yet. At this stage of the Cuban missile crisis people didn't realise how bad the situation was, so we probably don't have the full picture on the Ukraine war either.
The proxy war might be closer to Moscow than St Petersburg is. I don't think the Russians are fooled - the US just allocated more money than most countries GDP to this war, they may as well be directly at war. It isn't even a proxy war, the Russian army are suffering direct losses. Multiple Russian generals are dead [0]. Labelling it a proxy law is basically rules-lawyering in a way that is totally useless in the middle of an active war, the Russians are not going to react to this like it is some fight in the Afghan hinterlands or Somalia or something.
And this is in no way 'safer'. That is almost literally saying a Russian proxy war in Canada or Mexico would be less threatening to the US than a Russian missile base in Cuba. It is quite possible that when the dust settles we discover there was a 3:2 conversation where if it had been 2:3 humanity would be going extinct right now.
I'm not sure how people expect this war to end, but Ukraine being nuked is still an option if it goes badly enough for the Russian army. Unlikely, but war has a habit of becoming uncontrolled when the situation keeps escalating.
[0] https://en.wikipedia.org/wiki/List_of_Russian_generals_kille...
If you are offered the opportunity to go back in time and, say, kill Hitler, don't take it. You might come back to "Threads".
This is something that the film remake of "The Time Tunnel" left out. (The film is pretty OK.) If you really did have the ability to change the past, you'd need to be prepared to come back to a post-nuclear wasteland. So, your facility would need to have access to enough power generated on-site that you could keep going back and changing things (once? twice? thrice?) until you get it right and we're back to our world where the world wars haven't (yet) gotten past Number Two.