Does blood that flows for thirteen days after seven days of purity count as menstrual blood or as استِحاضة (istihada/non-menstrual vaginal bleeding), and what are the implications in both cases?

The woman's action of considering the returning blood as irregular bleeding (istihada) is correct. This is because it cannot be considered one single menstrual period along with the previous blood, as the total duration between them exceeds fifteen days. Nor can it be considered an independent menstrual period due to the purity interval between the two bleeding incidents not reaching the minimum duration (thirteen days according to the Hanbalis, or fifteen days according to the majority of scholars). Therefore, this blood is considered istihada, and the woman must pray, fast, and perform ablution (wudu) for each prayer after its time has begun. Her fasting is valid. In the future, she should consider what aligns with her regular cycle as menstruation and anything else as istihada.