Is the supplication mentioned in the question, and narrated from Imam Zayn al-Abidin ibn al-Husayn, which begins with "O Allah, I apologize to You for an oppressed person who was wronged in my presence and I did not help him...", sound?

This supplication does not contain any Sharia-prohibited elements, neither in its wording nor in its meaning, so there is no harm in supplicating with it, due to the general saying of the Prophet, peace and blessings be upon him: "Let each of you choose from supplication what is most pleasing to him, and then let him supplicate to Allah, the Almighty and All-Majestic." However, the superiority remains for what is taken from the Book of Allah and what is authentically narrated from the Messenger of Allah, peace and blessings be upon him.