Is it mentioned in Al-Bukhari that Fatimah (may Allah be pleased with her) died while she was displeased with Abu Bakr and Umar (may Allah be pleased with them), and what is the extent of the authenticity of that, if it exists?

Fatimah distanced herself from Abu Bakr until she passed away. Al-Bayhaqi, Al-Dhahabi, Ibn Kathir, and Ibn Hajar mentioned that Abu Bakr earned her رضا (رضا: contentment/satisfaction) and she was content with him before her death. The disagreement arose because she thought she had a share in inheritance, but Abu Bakr cited the Prophet's (peace be upon him) hadith: "We do not leave inheritance; what we leave is charity (sadaqah)." A number of Companions testified to the authenticity of this hadith. Thus, the truth was with Abu Bakr, due to his knowledge of the Prophet's hadith, and he is superior to Fatimah and all creation after the prophets. As for Umar, Al-Bukhari did not mention her anger towards him, and she passed away before his caliphate. He was held in high esteem by the Ahl al-Bayt, and Ali married his daughter Umm Kulthum to him.