Most companies that want to be that intrusive will just require you to have a top secret clearance and if you go through the process of that the government won't ask for access to things like email but people swear up and down with TS clearances that it felt like the people interviewing them in the process were aware of email communications.
I anticipate the higher you go the more intrusive it would get in the private sector but I seriously doubt any company would ask me for access to my email account. If they did I just would find a different company unless the pay was insane.
Anyway it's hard to know where you end up. The degree is in cyber security but I probably have to start at the bottom like anyone else and the opportunities could be in other places like networking .
I want to attempt to get closer and closer to protecting medical equipment though. They are very vulnerable and a serious threat if any terrorist wanted to target medical devices or specialize in them