Is it obligatory to cleanse the bathtub after performing ghusl following menstruation or a state of janabah? And what if I bathed while menstruating; is it then obligatory to cleanse it afterwards?

Perhaps the mother means reciting "Bismillah" (in the name of Allah) before performing ablution (wudu) and ghusl (definition) (ritual bath) after major ritual impurity (janabah (definition)) or menstruation (hayd), and reciting the Shahada (testimony of faith) after ablution. This is correct. It is disliked to engage in dhikr (remembrance of Allah) in the restroom. If she intends to utter these ذكرs within the restroom, then it is not prescribed. It is not obligatory to wash the place of bathing unless it becomes impure. The belief that a menstruating woman is prescribed to recite "Bismillah" and the Shahada over everything she touches is an innovation that has no basis.