What is the ruling of Islamic law and the expiation for forgetting medical compresses inside a patient during a surgical operation, which led to their death four months after their discharge from the hospital?

This situation is religiously termed "killing by causation." The determination of the causer is done by medical experts. The causer of the killing must pay the blood money (diyah) and offer expiation for accidental killing. If it is proven that the cause of death resulted from the negligence of the doctor, their assistants, or the nurses (male or female), then they are the guarantors. If it was due to the second operation, then the guarantor is the one who performed it. If the head nurse was responsible for counting the sponges and did not do so, then she is the causer and the guarantor. If the causer was ignorant of their duties, then they are the guarantor, based on the saying of the Prophet, peace be upon him: "Whoever practices medicine without knowledge is a guarantor."