Is this case considered istihadah, which necessitates making up missed prayers, knowing that the menstrual cycle is irregular?

Since the duration of the blood exceeded fifteen days, you are in a state of istihadah (non-menstrual bleeding), and the following applies to you:

1. If you had a previous custom (habit): What you experienced during your customary period is considered menses (hayd), and anything outside of it is istihadah. 2. If you did not have a custom, but you have valid discernment (tamyiz): What you distinguished as having the characteristics of menstrual blood (its color, odor, thickness, accompanying pain), and its duration is suitable for menses (a minimum of one day and one night, and not exceeding fifteen days), then that is menses, and anything else is istihadah. 3. If you had neither a custom nor discernment: You should estimate six or seven days of the month as menses, and anything beyond that is istihadah.

Upon the completion of the period you consider menses, perform ghusl (ritual bath) and pray, and you will have all the rulings of a ritually pure woman. You must perform ablution (wudu') for each prayer after its time has begun, taking precautions by tying a cloth or similar, and you may pray the obligatory prayer and any voluntary prayers you wish until the time expires or you incur another impurity.

You must also make up all the prayers you missed, thinking they were menses, because they are a debt upon you.