Is the Hadith: "Two types of mut'a were present during the time of the Messenger of Allah (peace and blessings be upon him), and I forbid them and will punish for them: mut'at al-Hajj (temporary marriage for Hajj) and mut'at al-nisa' (temporary marriage for women)," authentic?

Umar ibn al-Khattab, may Allah be pleased with him, prohibited two types of mut'ah: mut'at an-nisa (temporary marriage) and mut'at al-hajj (combining Hajj and Umrah (definition)). The prohibition of mut'at an-nisa has been authentically transmitted, and Ibn Hajar was of the opinion that his prohibition was not based on personal ijtihad (definition) (independent reasoning), but rather on established prophetic prohibitions that rendered it permanently unlawful. As for the prohibition of mut'at al-hajj, Ibn Hajar and An-Nawawi interpreted it as a disapproval, encouraging the performance of Hajj and Umrah on separate journeys, while acknowledging the consensus on the permissibility of ifrad (definition) (Hajj only), qiran (definition) (Hajj and Umrah combined with one ihram (definition)), and tamattu' (Umrah then Hajj with separate ihrams). Ibn Abd al-Barr and Iyad interpreted it as a prohibition against dissolving Hajj into Umrah for those who had already entered into Hajj, and not against the permissible tamattu'.