That 50 years would be for the dirtiest places affected. That would be a minute fraction of the globe, insignificant fraction of it. Nobody is going to bomb the hell out of nature-rich wilderness.
Bomb fallout is relatively short lived, even something like a 1Mt groundburst just downrange (3-5 mile or so) is going to be traversable in 1-3 months.
The biggest worry for radiation is power plant cores and spent fuel piles, the isotopes in there are the long lived ones. Not as “hot” but persistent. I was leaning towards that being a sword the deep state held via trojan infection of the water circulation systems that was mitigated.