What is the ruling on omitting the Salawat al-Ibrahimiyyah and the opening supplication (Du'a al-Istiftah) in supererogatory (Sunnah) prayers?

The Abrahamic prayer (Salat al-Ibrahimiyyah) is a Sunnah (recommended practice) and not obligatory. Uttering prayers upon the Prophet, peace and blessings be upon him, after the final Tashahhud is a pillar (rukn) according to the Shafi'is and in one narration from the Hanbalis. However, Malik, Abu Hanifa, and most scholars view it as a recommended (mustahabb) act, not an obligatory one. Omitting prayers upon the Prophet, peace and blessings be upon him, in Sunnah prayers does not invalidate them according to most scholars; therefore, it is even more so that their omission in the Abrahamic prayer does not invalidate them. However, one should not intentionally omit it.