Does the distinct odor found after a wet dream count as normal discharge that does not necessitate repeating prayers, or is it madhy (pre-ejaculatory fluid) which requires repeating them due to its impurity?

Doubt after completing an act of worship has no effect. It is not necessary to perform istinja (definition)' (ritual cleansing) from something one doubts whether it is madhy (pre-seminal fluid) or a vaginal discharge, because the default is that madhy has not been emitted. There is no harm in considering the discharge as a regular discharge and not madhy when in doubt. One must be cautious of obsessive whispering (waswasa).