Is there an authentic story or narration indicating that Salman (may Allah be pleased with him) sought to marry the daughter of 'Umar, and that 'Umar (may Allah be pleased with him) refused this proposal due to the disparity in lineage?

The books of siyar (biographies) and history mention the story of Salman al-Farsi's proposal to the daughter of 'Umar ibn al-Khattab. This story is narrated by Ibn 'Adiyy, Abu Nu'aym, Ibn 'Asakir, and Al-Dhahabi. However, all these narrations trace back to Al-Hajjaj ibn Farrukh al-Wasiti, whom Yahya ibn Ma'in and Al-Dhahabi deemed weak.

Ibn Qutaybah mentioned the story without a chain of narration, and it states that Salman became angry when it was said that 'Umar was being humble by marrying her off to him, so he swore he would never marry her.

Assuming the authenticity of this anecdote, it does not mention that 'Umar rejected Salman's proposal due to lineage.