There was a button and loop (croched?) on the outside, and a smaller button and loop on the inside. Neither was reinforced, but it’s a machine knit sweater at small gauge, and was designed to be an “easy” fit – so, it shouldn’t be putting strain on the buttons. That said, I might still reinforce the bigger, outside button just to be safe, since that one is really what’s holding it closed. The small inside button should be placed so that it’s just holding the inner panel in place, rather than pulling in any direction.
Also, if we really want to repicate the details of the sweater, note that the rolled collar starts at the same height as the buttons. Below that on both sides of the front, they seem to have about a 1" wide band in 1x1 ribbing. But I think it would be simpler to just continue the rolled collar all the way to the bottom.