That kind of algorithm doesn't show you anything besides the messages in your inbox. It's never making a decision to show you X instead of Y, it's just deciding the ordering in which you see them.

Modern social media is choosing from a vast pool of content and the algorithm's entire goal is to maximize engagement for monetary gain (at whatever cost to society). There's only so much "engagement maxing" you can do with an email sorting algorithm especially if the premise for an email inbox is that you'll always only ever see your emails and nothing else.

There are already a couple of answers for standard male programs, but if the male programs such as Gmail pushes up content to your inbox, save from Google then yes, that would be an algorithm that would qualify. I would really argue what you are describing is a filter rather than a content algorithm.

No, because mail programs can be configured by the user to turn off any algorithms that try to be smart.