The main reasons most observers are not super worried about nukes in the context of their invasion of Ukraine, is that MAD is still an effective policy against an all-out attack against NATO, and NATO (especially the US) has a credible red line of any attempt at a 'small-scale' use of nuclear weapons against Ukraine that will bring them into the war.
The main effect of nukes, though, is to make Ukraine's allies nervous about the collapse of the russian government, because that is a plausible situation in which nukes could be used. The US, especially, seems to by trying to help Ukraine win, but not win so hard that Russia collapses, and it's not obvious that a level of support exists that would satisfy both outcomes.