IIRC the superior auto mode can detect portrait and try to shoot a photo with shallower DoF. However, if you are expecting ridiculously shallow DoF (blurred background like Pixel 2/other dual lens shooter)... then we don't really have it.
Sony really ought to be able to do something like Pixel 2 does with all the sensors it sports. If XZ1 can do 3D creator with the sensors to measure depth, I am sure that there's a way to use that depth information to do some machine learning magic to blur the background. (We probably don't need it as anything that is not framed in the center tends to be blurry anyway)
