Is zakat obligatory on a sum invested in real estate that has reached the nisab and a hawl has passed over it, but it has not yet been received, its profits have not been settled, and it is unknown when it will be recovered?

The default rule is that it is not permissible to delay Zakat (definition) unless there is no money available, or what is intended for payment cannot be sold, in which case delay is permissible. You are obligated to pay Zakat on this money when a full year has passed, if its amount can be ascertained. Zakat must be paid on money designated for essential and fundamental needs and necessities, including money allocated for the marital apartment.