Is the prayer valid for someone who thought the verse of prostration was in Surat Al-Hijr and prostrated for recitation with the rest of the women, even though she caught the Imam in rukoo‘ and completed her prayer, then prostrated for forgetfulness after the tasleem?

Your prayer is valid, and you are not required to repeat it, because your performing the prostration of recitation, believing the Imam had prostrated, is considered an addition behind the Imam, and no prostration of forgetfulness (sujud al-sahw) is necessitated by it, as the Imam bears it on your behalf. Likewise, your performing the prostration of forgetfulness after the Imam's salutation, out of ignorance, does not invalidate the prayer because it is an unintentional addition.