I’m very sure that using a nuclear bomb on China or Russia in any capacity would escalate into a full exchange pretty quick.
Someday it will....with certainty.
Notably, Russian doctrine considers battlefield use of nuclear weapons as plausible and potentially advantageous without necessarily leading to a full nuclear exchange. Thus Russia might be tempted to use one or more small nuclear weapons to break the Ukrainian army without causing major civilian casualties while declaring that they do not intend a wider nuclear attack on the US or Europe.
Yet Russia would be much less inclined to try that if the US (or Britain) could swiftly counter with an equivalent small, limited nuclear attack on Russian forces in the field. Remarkably, US and Russian military strategists know well enough how each other think that there is a high degree of confidence in these calculations.
In our era of large and highly capable nuclear weapons stockpiles, a stable nuclear standoff between Russia and the US is essential to keeping the peace. It also helps dissuade more European countries like Poland, Italy, and Ukraine from developing nuclear weapons for their own sake.
Similarly, South Korea, Japan, Taiwan, and Australia refrain from developing nuclear weapons to counter China and North Korea because the US has that covered, more or less.
Any attack would have that effect. China and Russia are prepared to use a Samson option. It’s their only hope.