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You can take a tour of where they detonated the first and multiple bombs at Trinity twice a year.

The radiation levels at Trinity as well as Nagasaki and Hiroshima are far below what is natural in many other places.

My guess:

The “doomsday” nuclear apocalypse is real in so far that it will end the primary nations involved. We would cease to exist as an industrial, information, high tech society. The damage will be so great to industry, infrastructure, energy, communications, transportation, urban centers, the loss of life and in leadership/command and control will be so great that we as the US and Russia will basically be finished for the foreseeable future: https://nikemissile.org/targetmap.gif (Russia’s targets)

Older estimates from the Cold War, where they did some math and simulations and based things an what is likely a more realistic scenario (using realistic models for damage) put US casualties at ~25 million in the first 24 hours. Many more casualties would ensue within the next 30 days. The bulk of those in the next 30 days will die from radiation exposure or who survived but were badly burned etc.

Of course back then you had a lot of hardening: bunkers, shelters... which have mostly been removed (both private and public). But we also had a lot more nukes on both sides, but then again the stuff today is more accurate and reliable: https://www.researchgate.net/profile/Georgiy-Stenchikov/publication/26638523/figure/fig1/AS:394354716889091@1471032899509/top-Number-of-nuclear-warheads-in-Russia-USSR-the-US-and-the-total-for-all-the.png

Nonetheless, I think it would be devastating today - enough to “end us” in a practical sense. Einstein, often quoted as having said this, may not have, but it is true: “I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones.”

The probability of Russia using these is low (even now). Contrary to how we present Russia, they are doctrinal, have a very stable bureaucracy, a professional cadre of folks dealing with their nukes, and have safeguards in place. Where things get problematic is if fools like Lindsey Graham get their way: https://www.stripes.com/theaters/us/2022-03-04/graham-says-taking-out-putin-stop-ukraine-invasion-5225080.html If you have internal instability, a coup, then you get into a place where there are a lot of uncertainties and things you could have never predicted nor are in your and maybe even the leadership of Russia’s control. At that point is when I would be (very) concerned, i.e. all bets are off.

But the idea that it ends all life is a far stretch especially outside of those countries that were each others targets.