What is the authenticity of the mentioned chain of narration from Al-Waqidi, who claimed that Abdullah ibn Muhammad narrated to him from his father regarding the consensus of the Companions on Uthman, and who are Abdullah ibn Muhammad and his father?

This isnad (chain of narration) is not sound, because Al-Waqidi is matruk al-hadith (abandoned in hadith narration). Al-Waqidi narrated from Abdullah ibn Muhammad ibn Abi Yahya and Abdullah ibn Muhammad ibn Abi Farwah, both of whom narrated from their fathers. The correct view is that Abdullah ibn Muhammad is the son of Umar ibn Ali ibn Abi Talib, and he is trustworthy, as is his father. The defect in this athar (narration) lies in Al-Waqidi's condition, and then in the discontinuity, because Muhammad ibn Umar ibn Ali ibn Abi Talib's narration from his grandfather is mursal (has a missing link in the chain, specifically a Companion).