Is the authenticity of Ka'b ibn Zuhayr's poem "Bānat Suʿād" established?

The story of Ka'b ibn Zuhayr's delegation and his recitation of the poem "Bānat Su'ād" in praise of the Prophet, peace and blessings be upon him, is well-established. It has been mentioned by numerous scholars and transmitted in books of biography. Al-Bayhaqi narrated it in "As-Sunan al-Kubra" and "Dalā'il an-Nubuwwah," and al-Hakim in "Al-Mustadrak." Al-Hakim authenticated some of its chains of transmission.