Praise be to Allah
Wearing the burqa‘ is prohibited during ihram, whether that is in tawaaf or sa‘i, until one has exited ihram, because of the report narrated by al-Bukhaari (1707) from ‘Abdullah ibn ‘Umar (may Allah be pleased with him), according to which the Prophet (blessings and peace of Allah be upon him) said: “A woman in ihram should not wear niqab or gloves.”
The burqa‘ comes under the same heading as the niqab, so the woman in ihram is not allowed to wear the niqab or burqa‘.
Ibn Qudaamah (may Allah have mercy on him) said: Ibn al-Mundhir said: The fact that it is makrooh to wear the burqa‘ [in ihram] is proven from Sa‘d, Ibn ‘Umar, Ibn ‘Abbaas and ‘Aa’ishah, and we do not know of anyone who disagreed with that. Al-Bukhaari and others narrated that the Prophet (blessings and peace of Allah be upon him) said: “A woman in ihram should not wear a niqab or gloves.” But if she needs to cover her face because men are passing by close to her, then she may lower her garment from the top of her head over her face. That was narrated from ‘Uthmaan and ‘Aa’ishah, and it was the view of ‘Ata’, Maalik, ath-Thawri, ash-Shaafa‘i, Ishaaq and Muhammad ibn al-Hasan; we do not know of any difference of opinion concerning that. That is because of the report narrated from ‘Aa’ishah, who said: The riders would pass by us when we were in ihram with the Messenger of Allah (blessings and peace of Allah be upon him). When they came in line with us, one of us would lower her jilbab from the top of her head over her face, then when they had passed us, we would uncover our faces. Narrated by Abu Dawood (1833).
End quote from al-Mughni (3/154)
The hadith of ‘Aa’ishah was classed as saheeh by al-Albaani in Risaalat Jilbaab al-Mar’ah
Based on that, you made a mistake by wearing the burqa‘ during sa‘i. If that was done out of ignorance or because you forgot, then you do not have to do anything, but if it was done when you were aware of the ruling and you did it deliberately, then you must offer a fidyah, but your ‘umrah is valid.
The fidyah is to fast for three days, or feed six poor persons, or sacrifice a sheep and distribute its meat to the poor of Makkah and the Haram.
See also the answer to question no. 12516
And Allah knows best.