Is it obligatory to make up the prayers I missed previously, considering the subsequent bleedings from menstruation, or is it sufficient to adopt the new ruling that they are not menstruation from now on?

If you imitate those who say that the yellowish and brownish discharges are not menses, then there is no blame upon you, and you are not required to make up the missed prayers. Some scholars have made it easy to adopt some of the concessions of scholars out of necessity.