I do not question that Sharbeldam's assumptions about the composition of the phases are not true, but I recommend a lot of restraint on the conclusions.
During the butanone extraction, the aqueous phase contains almost 30% butanone, and the organic phase about 10% water (as Hollytara pointed out). Therefore, all reaction products and unreacted substrates can be in both phases in unspecified proportions, all the more so because sodium or potassium iodide dissolves quite well in butanone.
The aqueous phase has a slight excess of potassium carbonate and sodium hydroxide, which can affect the reduction of the solubility of NaI and KI in water by displacing these compounds into the organic phase. No conclusions can be drawn based on the density of the NaOH solution added, because it has reacted to a large extent to form an additional, although a small amount of water.