The nuclear paper tiger
The above video makes some essential points about the white-knuckle calculation involved in military aid to Ukraine -- how much help can we give without pushing Putin to the point where he resorts to the nuclear option? It makes sense given everything we know about how Russia's government and society operate, and what the Ukraine war has shown us about the general condition of the Russian military. I would urge you to watch it despite its length (23 minutes) since it goes into much more detail than I can here.
To summarize: Regular maintenance on nuclear weapons, and on the ICBMs that carry the long-range ones, is extremely complex and very expensive (the US spends fifty billion dollars a year -- almost equal to Russia's entire military budget -- on maintenance for a substantially smaller nuclear arsenal). There's no reason to think that maintenance on Russia's nuclear weapons has not suffered from the same problems as everything else in the Russian military has -- incompetence, neglect, corner-cutting, allocated money not getting spent for the intended purpose because it was embezzled, and so on. The Russian military has also long had a mentality that there was never going to be a major war, so it didn't really matter whether equipment was maintained properly.
This being the case, after a third of a century since the collapse of the Soviet state, most of Russia's nuclear weapons probably do not work. No one -- not even the Putin regime -- knows how many still do work or which ones, but they are doubtless aware of the general extent of the problem.
Of course, even a small number of still-working H-bombs could have catastrophic effects, since just a single one can annihilate an entire metropolitan area. If Russia launched enough ICBMs, some of them would probably reach and destroy their targets. The loss of Paris or London or New York City would obviously be intolerable for the West. However, the West would survive as a set of functioning societies, and such an attack would trigger massive retaliation by the NATO nuclear powers (the US, France and the UK). And our nuclear weapons do work. Any scenario where Putin went nuclear could have only one outcome -- the West would mostly survive, while Russia would be erased from the face of the Earth.
Russia would face more prosaic risks too. Malfunctioning nuclear weapons, if launched, might well explode in the silo or crash soon after launch. Their warheads would not detonate, but would certainly be badly damaged, spreading radioactive contamination across Russian territory. If Putin launched fifty ICBMs in the hope that two or three would make it to destroy their targets, he might well do more damage to Russia than to the West.
Since Putin knows the above is almost certainly the reality, the chance that he would actually order a nuclear attack is essentially zero -- and even if he were crazy enough to do so, others in the Russian military and political elite would likely remove him to prevent the order from being given or carried out. He will threaten and bluster in an effort to intimidate us, but he dares not actually carry out such threats. Western governments are wise to be cautious, since Putin might act irrationally under extreme pressure, but in any realistic scenario, it's very unlikely that we face a real risk of a Russian nuclear strike.
Here are two more videos, on tanks and the air force, which illustrate just how bad the situation in Russia really is, and what that implies about the rotted-out culture of incompetence and corruption endemic to authoritarian states:
The Russian economy is less than two-thirds the size of the British economy. There is no way that Russia can match the entire West. If anything, the problems discussed here are probably getting worse with time, due to all the shortages and disruption caused by sanctions.
Finally, it's almost certain that everything said here about Russia applies even more to China -- a totalitarian rather than authoritarian state, even more centralized, even more riddled with corruption and incompetence.
Historically, one dictatorship after another has risen to challenge the democracies, and every one of them has gotten its ass kicked onto the garbage heap of history. We will dump Putinist Russia there as well.