Russia is a China's client state at this point, and China is very interested in keeping nukes taboo. They are so worried their own army is only allowed melee weapons in border skirmishes with India. There is no way a demonstrative breaking of the taboo would not get Putin's leash yanked, so even that remote possibility (that has nothing to do with WW3) is extremely improbable and would only hasten Russia's defeat. Unless, of course, our politicians use it as an excuse to abandon Ukraine.
Also, no one is "pushing Russia's back against the wall" in Ukraine, there are no M1A2s speeding to Moscow. Russia understands it perfectly well, too, denuding their borders with NATO to throw more soldiers into the meat grinder.
> the fact that we can't assume these people are acting rationally
I think this meme is largely a cop-out. A person just doesn't get to be a leader of a country by acting irrationally. They might interpret things differently or have different priorities, they might even put on an act of irrational buffoonery, but it's different from being "irrational". However, to see the rationality of their actions requires putting yourself in theirs shoes, which is uncomfortable and/or requires a deeper understanding, so it's easier to just write their behaviour as "irrational".
Putin is perfectly rational. The empty threats are working (as evidenced by this thread), there is no risk of a strategic exchange (because the actual signalling on the ground is one of business as usual), and Western politicians are successfully convincing their voters that they drag their feet because WW3, not because actually stopping the war (eg deploying a NATO peace keeping force) would incur a substantially higher domestic cost.
We don't really talk about potential North Korean aggression in WW3 terms, do we? We shouldn't do that in Russian case either.