With the default brush settings, the brush alpha is incorrect (Sharp shape: OFF).
In the screenshot below i used an alpha with smooth edges & when "Sharp Shape" is OFF, the result is incorrect because it has hard edges even though it's supposed to be a soft edged brush.
When "Sharp Shape" is ON, the brush has smooth edges like it's supposed to, but when the brush stroke intersects with itself & you don't lift up the pen, it creates weird looking corners.
With "Sharp Shape" OFF, the self intersect result is correct but the edges are hard even though it's a soft brush.
There is no way to get the correct result, either the brush alpha has hard edges even though it's supposed to have smooth edges or the self intersect result is incorrect.
(All strokes in the screenshot are drawn with the same alpha & same brush size, using the "depth & opacity" brush)