I don't really understand all the talk about Putin using a "nuclear" weapon on Ukraine

That seems really stupid tactically to me, Putin appears to have sold this as a war of liberation/denazification to his citizens, so nuking the country seems like it's a non-starter. If Putin decides to use a weapon of mass destruction, chemical weapons seems far more likely and bring with it a lot of plausible deniability (eg it could be blamed on terrorists). But even that seems highly unnecessary, Russia already has the means to disrupt the energy, export, food production and water supplies of most of the country, they could preserve the infrastructure and make the urban areas unlivable with strikes targeting power stations, ports, water treatment, dams, railroads, heck even a cyber strike might accomplish the same goals - going to weapons of mass destruction just doesn't seem like it'd make sense in comparison