This bike (the small one) is even designed for double that amount (60kg). As common as non-motorized post bikes are already, I guess you learn to deal with it.

1: https://windsorsradweg.files.wordpress.com/2012/01/cropped-d...

Notice that the handlebars are tilted while they front basket is straight. They're not attached to the forks, they're attached to the frame. While that's still a lot of weight (and heaven help you if it shifts during a turn) it's not going to have the same feeling as a basket which is attached to the bars.

They're sturdy containers along the center of the bike. I'm sure it feels a little different, but nothing too disconcerting. Besides, once they've reached their destination area, they're stopping every 20 meters to deliver mail to a different building.

They also have small support wheels that can be deployed to move the short distances from door to door.

I have an electric bike with front and rear racks plus rear side baskets. With them all loaded up the bike handles much differently but isn't hard to control. You get used to it quickly.