What is the authenticity of the hadith mentioned regarding the virtue of the prostration of thankfulness (sujud al-shukr)?

Prostration of thankfulness (sujud al-shukr) is recommended upon the occurrence of a blessing or the warding off of an affliction. It consists of a single prostration, and its recommendation has been affirmed by the actions of the Prophet, peace be upon him, and his companions.

The Prophet, peace be upon him, prostrated in thankfulness when he was pleased, and Ka'b ibn Malik, Abu Bakr, and Ali ibn Abi Talib, may Allah be pleased with them, prostrated for similar reasons.

As for the hadith mentioned in the question, none of the trustworthy hadith scholars narrated it. Rather, some Shiite books, which are filled with fabricated hadiths, mention it. Its chain of narration is weak; therefore, it is not permissible to attribute it to the Prophet, peace be upon him.