Does the RAW format save the kind of information that the software uses to guess at bokeh (depth sensors, multiple lenses, multiple shots, defocused pixels)? Or is there some other format that could save all that info, so you could really use the phone but do the processing later?

There’s no, but there isn’t really a need. The R package mentioned in a comment in this thread achieves a similar effect using no additional data.

Ray tracing will suffice!

It shows a hand made depth map. You can't just 'raytrace' a 2D image and magically add depth of field.