Are the secretions that appeared after the first instance of vomiting considered wady? If so, can the jurisprudential opinion that permits the prayer of one ignorant of impurity be adopted, especially given the unknown number of prayers performed in those clothes?

If you judged the initial discharge to be vaginal moisture (rutubat al-farj), then your prayer is valid and does not need to be repeated, even if it later becomes clear that it was not. And if you prayed with an impurity you were unaware of, your prayer is valid, because avoiding impurity in prayer is conditioned upon knowledge and and ability.