Just like for road accidents, death is a wrong measure, as it really depends on your health, i.e a 20 years forager will survive whereas an 80 years old one would die. Many mushrooms are liver-toxic, so if you already have hepatitis (very common in Russia), you're probably more prone to die from a poisonous one.
Intoxication leading to hospitalization is a better measure.
Given approximately everyone's heard of it, and warnings about it, but also that I don't personally know anyone who tells me that they personally do this, my guess is in the order of 1% of the population. Might be more, might be less.
1% of Russia would be 1.5 million (and given this thread, 412k for Ukraine).
According to the 2014 survey https://fom.ru/Obraz-zhizni/11711 , 75% Russians have ever went to pick up mushrooms, and 40% have done it in the last year before the survey. 8% personally know people who suffered from mushroom poisoning.
This corresponds to my expectations: I'm from a neighbouring country, Belarus, and basically almost everyone around me has been picking up mushrooms.
That's not just a culinary experience, but a way to relax: go to forest, disconnect from the world, unwind. (People also pick up blueberries and lingonberries for the same reasons.)
Oh, and my classmate died from mushroom poisoning.