Is interrupting the circumambulation (tawaf) for ablution (wudu), then resuming it and performing the ritual circumambulation (sa'i) – valid? And what should have done?

The majority of scholars stipulate purity for circumambulation (Tawaf), just as they do for prayer, based on the hadith: "Circumambulation of the House is a prayer," the Prophet's (peace be upon him) own practice, and his command to 'Aisha to refrain from circumambulation while she was menstruating. Meanwhile, some scholars hold that purity is not a condition, arguing that the hadith "Circumambulation of the House is a prayer" is attributed to Ibn 'Abbas (i.e., it is a saying of a Companion, not the Prophet), the Prophet's (peace be upon him) actions do not necessarily indicate obligation, and 'Aisha was prohibited due to her menstruation and the general prohibition of a menstruating woman entering a mosque. While the second opinion has strength, the first is more cautious and preferable. As for Sa'i (the ritual walking between Safa and Marwah), ablution is not required for it, and a menstruating woman is permitted to perform it.