What are the months of Hajj?

Imām Ibn al-Jawzī (d. 597/1201) summarized the scholars' opinions in his book "Zād al-Masīr" as follows:

1. Shawwal, Dhul-Qa'dah, and the first ten days of Dhul-Hijjah. [Ibn Masʿūd, Ibn ʿUmar, Ibn ʿAbbās, Ibn al-Zubayr, al-Ḥasan, Ibn Sīrīn, ʿAṭāʾ, al-Shaʿbī, Ṭāwūs, al-Nakhaʿī, Qatādah, Makḥūl, al-Ḍaḥḥāk, al-Suddī, Abū Ḥanīfah, Aḥmad ibn Ḥanbal, and al-Shāfiʿī, may Allah have mercy on them]
2. Shawwal, Dhul-Qa'dah, and the entire month of Dhul-Hijjah. [Also narrated from Ibn ʿUmar, ʿAṭāʾ, Ṭāwūs, Mujāhid, al-Zuhrī, al-Rabīʿ, and Mālik ibn Anas] Ibn Jarīr al-Ṭabarī explained that those who hold the second opinion mean that these months are not for ‘Umrah, but only for Hajj, even though the rituals of Hajj end with the end of the days of Mina (13th Dhul-Hijjah). They preferred to perform ‘Umrah outside these months.