That probably not as true as you think. While yes there is radiation, the radiation would not linger as the atmosphere would dissipate most of the radiation
The EMP would shut off electronics for whatever country this thing is detonated over. Dependent on yield of course.
And of course the blast wave would knock many satellites, maybe even ISS, into unpredictable patterns. Most will burn up in the atmosphere, some of the most durable satellites will not. Some will ricochet to other satellites. It will be a regular FFA of countries trying to dodge space debris for the first 3 hours.
When the dust settles and citizens are without news, or internet, or sports, or podcasts, or entertainment what will happen then? I imagine not many citizens US or otherwise will be happy with Russia at all.