Thanks for taking the time to make a long comment with some links.
I wasn't wondering about the research, I was curious if you were referring to supplements when you used the word overload.
The overall research is pretty much on the fence about eating healthy foods like tofu and how that affects menopause symptoms, with specific results being it helps some people, others see no effect and even some others see symptoms worsen.
One thing I that became clearer for me from your links is that baby soy formula is bad. That makes senses, giving a rich source of phytoestrogens a a crucial time in development when the normal diet contains zero phytoestrogens is at best misguided. But once an infant transitions to regular food it doesn't seem like eating even large amounts of soy beans is a problem.
The numbers from China and Japan seem to back that up, their average diets are healthier overall, include lots of soy beans and avoid soy baby formula compared to the average diet here.
I'm tempted to believe that here the problems you're referring to (compared to China and Japan), on average come from a conjunction of soy baby formula, overall less healthy diets, soy supplements, be they protein supplements or all of the soy based supplements that are used in a lot in foods and especially in processed junky foods, and from our on average higher BMIs and the effect that can have on our hormonal balance.