Is the surgeon held Islamically accountable when performing a kidney transplant if it becomes apparent that the sale of the kidney was done by concealing the truth? What is the Islamic ruling if the donor confesses to this during the operation? And is it Islamically permissible for the patient to give a gift to the donor in return for their sacrifice?

It is not permissible to sell human organs. However, there is no harm if the donor receives a reward or a gift, as long as he does not covet it. If the donor and the patient lie and conceal the reality of buying and selling, then there is no sin upon the doctor and those assisting him in performing the operation, because the default assumption is that a Muslim is truthful and trustworthy. However, if the donor admits before the operation that he is selling the kidney, then the medical team must refrain from the operation unless it is a case of necessity.