To what extent is the hadith "It is written on every private part who will copulate with it" authentic?

The aforementioned Hadith, "It is written on every private part who will penetrate it," is not authentically attributed to the Prophet, peace and blessings be upon him. However, the meaning that Allah has written and predestined everything is correct, as evidenced by the Hadith in Muslim: "Allah ordained the measures of creation fifty thousand years before He created the heavens and the earth."

Shaykh al-Islam Ibn Taymiyyah stated that this Hadith is not authentic and is not from the words of the Prophet, peace and blessings be upon him, and that Allah wrote everything that His servants would do before they did it. Similarly, Al-Ajluni said that it is not a Hadith, but rather a saying of the Arabs.