Is it obligatory to make up for missed prayers due to not performing ghusl after semen discharge, given ignorance of the difference between semen (mani) and pre-seminal fluid (madhy), and not remembering the number of missed prayers?

The characteristics of a woman's maniy (spermatic fluid) and the difference between it and madhiy (pre-seminal fluid) have been explained in previous fatwas. If you are certain that what exited from you is maniy, then ghusl (ritual bath) becomes obligatory upon you. If it is madhiy, then wudu (ablution) suffices. If you are in doubt, you may choose [between ghusl and wudu, or consider it madhiy]. If you are not certain that your previous prayers are invalid, then the default assumption is their validity, and doubt after completing an act of worship has no effect. If you are certain that you prayed without the obligatory purification, there is a difference of opinion regarding making up those prayers. The more cautious approach is to make them up, and the method for doing so has been explained in a previous fatwa.