What you will get is a web application you get to sign into to actually get your mail, and you will receive a notification mail in your regular email inbox stating that you have received mail (but not from whom, or what the subject is, because that is privacy sensitive information), so that you know that you should go and get it yourself via the web application.

This is what every digital 'inbox' that isn't email has done thus far. This is in fact exactly what the Dutch government has done with their digital inbox which is intended to replace physical letters from services like the revenue service and municipalities. Thankfully that monstrosity is optional (for now).