Is the white discharge that appeared twice after ghusl following menstruation considered a white discharge (qassah bayda’) that necessitates ghusl, or is it madhy (pre-seminal fluid) that does not necessitate it, especially since the questioner is accustomed to dryness indicating purity?

A woman is not required to perform ghusl (definition) (ritual bath) if she has not experienced anything that necessitates it. The discharge she observed could be ordinary vaginal moisture. If she is unsure whether it is madhi (pre-seminal fluid) or a pure discharge, she may choose and assign to it the ruling she wishes.