Depth of field is proportional to the aperture/focal length^2
For a given field of view your focal length must change for different sensor sizes so effectively you see a shallower depth of field.
While computational imaging is doing amazing things right now, I've yet to be impressed by any sort of portrait mode, they simply do a mediocre job at creating a realistic sharpness falloff and fail far too often at identifying the edges of a subject. Once they get it right however, they could theoretically do some absolutely amazing things by simulating different bokeh and as small of a DoF as you could ever desire.