I don't think Putin will use nukes, he knows the cost of the clean up after the Chernobyl fiasco, this is going to get ugly real fast .
Low yield battlefield air burst nukes have much less fall out. They have a much larger stockpile than the US of these types of weapons. It was difference in strategic choices. I think the idea is the us of a battlefield nuke would put your opponent in a very difficult situation. Do you go full MAD(Mutual Assured Destruction) or just suffer the losses.
https://en.wikipedia.org/wiki/Tactical_nuclear_weaponChernobyl was so dirty because is smoldered for ever and the smoke was highly contaminated.
Nuke strategy and tactics are new and untried just as Blitzkrieg was new and untried.