Is it obligatory to ascertain that madhy (pre-seminal fluid) has exited before every prayer or after every adhan (call to prayer) before commencing the prayer, especially since madhy exits without arousal and sometimes without feeling its exit?

Al-madhy (pre-seminal fluid) nullifies ablution, and it is obligatory to wash it and purify whatever parts of the body and clothes it has touched, upon certainty of its presence. There is no need to search for it merely based on doubt, because certainty is not removed by doubt, and delving deeply into searching for purity is an innovation. If you doubt that something has exited, do not pay attention to the doubt. However, if the madhy is continuous, then it is considered sals (incontinence), and in that case, one must perform ablution when the time for prayer enters and pray according to the situation.