Is a forty-day spiritual retreat (chilla) part of Islam?

The forty-day retreat has a basis in the hadith.

In tariqa, many Sufi masters have adopted the practice of remaining in seclusion for forty days. This rests on the words of the Prophet ﷺ: “Whoever worships Allah for forty days with sincerity, fountains of wisdom shall gush forth from his heart and from his tongue”. [Musnad ash-Shihab 1/285]

And there is the Prophet's ﷺ own example. Ayesha may Allah be pleased with her, the Mother of the Believers, narrated that before the revelation commenced, the Messenger ﷺ became attached to seclusion in the cave of Hira and engaged in worship for several nights in succession without going back to his family. [Sahih al-Bukhari 3]