What is the authenticity of the hadith narrated by Ahmad from Abu Hurairah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) prayed while he was in a state of major ritual impurity (junub), having forgotten?

The books of Sunnah mention an incident where the Prophet (peace be upon him) remembered, while praying or before it, that he was in a state of major ritual impurity (janabah). So, he departed, performed ghusl (ritual bath), then returned and led the people in prayer. This incident has been narrated in different wordings:

Before the opening takbir (takbirat al-ihram): The Prophet (peace be upon him) remembered his state of janabah before the opening takbir. This wording is found in Sahih Muslim and Al-Bukhari. After the opening takbir and entering the prayer: The Prophet (peace be upon him) remembered his state of janabah after he had pronounced the takbir and entered the prayer. This wording is found in Sunan Ibn Majah, Al-Daraqutni, Al-Bayhaqi, and others. Its authenticity is disputed due to weakness in some of its chains of narration, but there are other corroborating evidences that strengthen it.

Summary: The discrepancy in narrations can be reconciled by stating that the incident occurred multiple times: once he remembered before the takbir, and another time after it. There is no issue with this, as the Prophet (peace be upon him) was a human being who forgot, and he was only infallible regarding the revelation.

Extracted Jurisprudence (Fiqh): This hadith is evidence that the prayer of the congregants is not affected if the imam leads them while forgetting he is not in a state of ritual purity. Only the imam needs to repeat his prayer, not the congregants. This is what Al-Shafi’i indicated, and it is agreed upon by the majority of jurists from various regions and the people of hadith.