What is the ruling on one who doubts whether he completed the Abrahamic prayer by saying "O Allah, bless our Prophet" or "O Allah, Allah, bestow Your grace upon our Prophet," so he repeated the doubted part as a precaution? Does this necessitate prostrations of forgetfulness (sujood as-sahw)?

If you are unsure whether you completed the Salat upon the Prophet, peace and blessings be upon him, then recite the part you are doubtful about. You are not required to perform the prostration of forgetfulness (Sujud (definition) al-Sahw). You should focus on your prayer to avoid obsessive thoughts (Waswasah). We draw your attention to the fact that the wording of the Ibrahimiyya Salat in the Two Sahihs (Bukhari and Muslim) does not include the phrase "O Allah, send prayers upon our Prophet and bless our Prophet." Rather, its text in Bukhari is: "O Allah, send prayers upon Muhammad and upon the family of Muhammad, as You sent prayers upon Ibrahim and upon the family of Ibrahim. Verily, You are Praiseworthy, Most Glorious. O Allah, bless Muhammad and the family of Muhammad, as You blessed Ibrahim and the family of Ibrahim. Verily, You are Praiseworthy, Most Glorious." Therefore, one should adhere to the established wordings of the Hadith (definition).