What is the expiation for someone who completed the circumambulation (Tawaf) out of embarrassment after their ablution (wudu') was broken, and then performed 'Umrah a year later?

Scholars have differed regarding the ruling on ritual purity (tahara) for circumambulation (tawaf). The majority opinion is that it is a condition for its validity. Therefore, if ritual purity is broken during tawaf, one must exit to perform ablution (wudu) and then complete the tawaf. If one does not do so, they remain in their initial state of ihram, and the second 'umrah does not become valid. Whereas some scholars, like Ibn Taymiyyah, held the view that ritual purity is not a condition for the validity of tawaf, and that whoever loses purity during it can complete it. According to this view, your first 'umrah is valid, and nothing is required of you, while the second 'umrah is supererogatory (nafilah).