Is my action correct if I doubted my prayer then became certain after the prostration of forgetfulness that I had completed it, so I repeated the prayer due to the addition of a prostration of forgetfulness?

If a worshipper doubts during prayer whether they have omitted a pillar (rukn) of the prayer, they must perform it; otherwise, their prayer becomes invalid, because the default assumption is that it was not performed. However, if they contented themselves with the prostration of forgetfulness (sujūd al-sahw) and then became certain after the prayer that they had performed the pillar, scholars have differed regarding the invalidity of the prayer, with some preferring the view of invalidity. As for adding two prostrations of forgetfulness out of ignorance, this does not invalidate the prayer. And whoever doubts whether they have omitted a Wajib (obligatory act) is not required to perform the prostration of forgetfulness, according to the preferred view.