Is it obligatory to make up the prayers of another day, as a precaution, after performing ghusl and making up the prayers of a full day, if I am not certain when the bleeding stopped and menstruation ceased?

A woman must check for purity before the prayer time expires. If she becomes pure, she should perform ghusl and pray. As for past prayers whose obligation to make up you are unsure of, you are not required to make them up, because the default assumption is that menstruation continues as long as you doubt the occurrence of purity. If she sees purity, she must promptly perform ghusl and is not required to make up any of the prayers.