Is ritual purity (wuḍūʾ) required for the Duha sitting after its invalidation, or can the sitting be completed without ritual purity?

Purity (taharah) is not a condition for sitting in the prayer area (musalla) and engaging in remembrance of Allah (dhikr) after the Fajr prayer until sunrise, because dhikr does not require purity. Nevertheless, it is better for a Muslim to remember Allah while in a state of purity.

As for the virtue of a worshipper remaining in their prayer area, the continuation of purity is a condition for achieving this, and for the angels' seeking forgiveness and supplicating for the worshipper, because the "hadath" (impurity) mentioned in the hadith refers to the nullification of purity.

If a Muslim's purity is nullified unintentionally, and they leave to perform ablution and then quickly return to their sitting place, this will not prevent them from receiving the full reward, Allah willing.