I assure you that if the Russians are the first nation in three quarters of a century to use a nuclear weapon that a whole bunch of other nations will immediately jump in.
Not necessarily. Because that had been the largest worry since people started to realize why MAD worked. And largely why the idea of a "limited nuclear exchange" was largely an unwinnable concept.
Honestly, I think if Russia used only 1 or 2 and on battlefield targets, the rest of the world would respond conventionally. Primarily out of fear of escalating an even more severe nuclear attack or exchange.
However, if Russia was to nuke another country that it is not actively in conflict with, say Birmingham, UK in the hopes of intimidating England to stay out, then a nuclear exchange might then advance to two more bombs on the UK, then 4 at Russia, until it becomes a free for all.
This has been studied and gamed extensively for well over 60 years now. And interestingly, there were two books that both went over it, and had almost the same resolution.
The first is "The Third World War: August 1985" by Sir John Hackett. In it, he had the Soviets launch a nuke at Birmingham as a warning to NATO to stop fighting their attempt to annex all of Germany. And if I remember correctly, the US, UK, and France all sent a nuke in response to a Russian city. Both as a show of solidarity, and as a warning that any further nukes would result in threefold retaliation.
And of course there is "Red Storm Rising", but Tom Clancy. If I remember the Politburo was about to order a strike against a British city, when an internal coup ended the madness as the more sane leadership knew it would not end at just one nuke.
But I could see for example multiple nations declaring war on Russia if it did so, then responding in concert conventionally.
