Does the Italian cover both uses?
Whose soap? is distinctly a question of selection, with the owner of each of the soaps already known. Person A says, "You've run out? Use someone else's soap." Then person B asks, "Whose soap?" In this situation "Whose is the soap?" is incorrect.
Whose is the soap? indicates there is some soap present, the owner of which is not known. In this situation "Whose soap?" is incorrect.
I can conceive the idea that both uses might be phrased the same in Italian. But I don't know this to be true. Is it?
Very awkward, it is not a correct structure, as English speakers we do say 'whose soap is this?'.
As a native English speaker this is really not a proper structure as we never say "whose is the soap?".
I would like to point out that there is colloquial and formal English. This translation you could use in colloquial but I not in formal English. While this Duo is not perfect, realize it is working through a computer. Sometimes the "word bank" is incomplete and I just type in the missing words. "Di chi" does translate as "whose" in an Italian/English dictionary.