What is the ruling on someone who prayed all the prayers of their day then discovered they had a wet dream (were in a state of major ritual impurity), so they repeated all the prayers secretly, by making up the missed prayer of the previous day after praying the prayer of the same time on the following day? And does anything result from their action?

If a person makes up for the prayers they missed, their responsibility is discharged, whether they make them up silently or audibly. Audibility and silence in their respective places are commendable, not obligatory. Whoever deviates from the Sunnah (definition) has missed out on the virtue, but their prayer is valid. It is appropriate for someone who missed a prayer and wishes to make it up to observe the proper sequence between this missed prayer and the current prayer. This is preferable to avoid disagreement, even though it is not obligatory.