Is the prayer of one who has recited the entire Qur’an multiple times during Qiyam al-Layl considered valid, despite her not knowing the permissibility of performing Sujud al-Tilawah during prayer and thus not performing it?

Your prayer is valid, and its validity is not contingent upon the prostration of recitation (Sujud (definition) al-Tilawah). The prostration of recitation is a supererogatory act, not obligatory, according to the majority of scholars, for both the reciter and the listener, whether in prayer or outside of it. Imam Al-Bukhari narrated from 'Umar ibn Al-Khattab, may Allah be pleased with him, that he said: "Whoever prostrates has done well, and whoever does not prostrate incurs no sin." Al-Jama'ah, except Ibn Majah, narrated from Zayd ibn Thabit his saying: "I recited 'Al-Najm' to the Prophet, peace and blessings be upon him, and he did not prostrate during it."