Is ritual purity permissible in the Farewell Tawaf and Sa'i while wearing shoes, and what are the consequences if it is not permissible?

It is permissible to perform the circumambulation (Tawaf) and the ritual running (Sa'i) while wearing clean sandals. However, it is preferable not to perform Tawaf with them to avoid defiling the mosque. A pilgrim in the state of ihram may circumambulate with his sandals if he has wounds or similar issues, and there is no harm in it for him, provided he ensures their cleanliness, based on the saying of the Prophet, peace and blessings be upon him: "When one of you comes to the mosque, let him look [at his sandals]. If he sees any filth or impurity on his sandals, let him wipe it off, then let him pray in them."