I have tried cold email outreach with .edu accounts. My theory was that deliverability + open rate would be improved. And maybe the added trust of a .edu email would make my pitch more convincing. I was able to send somewhere between 100-200 (don't remember) emails per day for several months before eventually the university shut the account down. My guess is that I was automatically suspended by Gmail.
On one hand there could be trust benefits because .edu emails are so rare and people generally want to help students. On the other hand, the .edu email marks you as young and this could make you look inexperienced / less trustworthy in the eyes of the recipient.
I did not notice any changes in open rates or conversions. At least for my use case the .edu email was not a silver bullet.
I imagine a .edu with a female name could work quite well in certain adult niches.