I think it's more of an aesthetic or fashion decision than something inherently functional. Anyway, here's an argument.
Most of the components in an interface are framed within an orthogonal grid, such as the example in the question. In fact, the screen itself responds to Cartesian axes, we have not yet reached the oval or formally fluid screen. This image shows a basic layout grid with its respective items where both elements are clearly perceived:
This type of layout not only emphasizes the structure but interferes with a clear perception by adding a third element: the gutter. The grid alone, while simple, is perceptually too complex:
Sometimes the designer prefers to avoid the clear preponderance of the base grid or eliminate these gutters from the root to simulate a less structured, more natural design or simply give more relevance to the items. The extreme would be the item with a fully rounded frame or circle:
By eliminating the edges of the shapes, the optical center becomes more visually relevant, each item is placed at the intersection of the axes of the structure lines (a). The gutter gets totally diluted. Perceptually it's much simpler:
The orthogonal shapes with rounded corners try to weaken the marked Cartesian axis of the base structure. But, while the gutter is still clearly perceptible, the rigidity of the union between the curve and the side generates a new element: the grid illusion.
Smooth corners are an optical arrangement to simplify visual perception, trying to avoid the mismatches described without dispensing with the use of orthogonal shapes, replaced by circled squares: squircles.