What is the ruling regarding someone who doubted their second prostration during the final Tashahhud of the Fajr prayer, so they interrupted the Tashahhud, prostrated, then completed it, performed the prostration of forgetfulness, and then said the taslim?

What you did by building upon certainty, performing the second prostration, and making the prostrations of forgetfulness, is correct. It is sufficient for you to perform the second prostration without making the supplication between the two prostrations if you had made it previously. Al-Shirbini said: "If, at the end of his prayer or after finishing it, and the interval was not customarily long, and no impurity attached to it, he became certain that he had omitted a prostration from the last unit of prayer, he should perform it and repeat his tashahhud." Your prayer is valid, and you do not need to repeat it.