Is it permissible to perform surgery to correct a birth defect that narrows the airway in the nose, with the request that the surgery also be cosmetic at the same time, knowing that there is a desire to cosmetically alter the tip of the nose due to dissatisfaction with its appearance, and that the cosmetic procedure will only be performed if it is linked to the removal of the defect that narrows the airway?

There is no objection to treating a defect with surgery. As for performing an accompanying procedure to beautify the tip of the nose, it is permissible if the deformity has reached the extent of a repulsive defect, in order to remove it and beautify the appearance. However, if it is less than that, it is not permissible to alter Allah's creation for the purpose of beautification and increasing beauty, unless a person has a disfiguring and unsightly appearance, in which case there is no blame on him for removing the disfigurement.