Is it a condition for the leader of the Muslims or the Caliph to be from the Quraysh, and are the Ottoman Caliphs considered sinful for not appointing a Qurayshi?

The scholars are unanimous that the Caliph of the Muslims must be from Quraysh, citing the saying of the Messenger of Allah, peace and blessings be upon him: "The Imams are from Quraysh," and that the Arabs follow Quraysh in good and ill. Abu Bakr Al-Siddiq used this hadith as an argument against the Ansar on the day of Saqifah. The wisdom behind this is that Quraysh is the best of the Arab tribes, and it is a place where virtuous people, sound judgment, and rectitude are likely to be found, as mentioned in prophetic hadiths. As for the Muslim rulers who act as deputies for the Caliph, it is not a condition for them to be from Quraysh.