As someone approaching the subject from the Maimonidean angle, it amazes me how people attribute innovations to Rambam’s son that are actually earlier described in Rambam’s works, and much of which is first mentioned in the classical rabbinic literature.
Many things that they attribute to Islamic Sufi influence are clearly revivals of the documented earlier Jewish practice, for those who are familiar with the MT laws of prayer and the Guide’s chapters on prayer and contemplative meditation.
Which is not to say that there were no Islamic Sufi influences on Rambam or his son. The Sufi literature that Rambam read in Andalus is well-documented, as are its influences on his thought. Similarly, his son was no stranger to quoting the Quran alongside the Tenakh, along with the relevant insights of well- and lesser-known Islamic Sufis. But these influences supplement and adorn a Jewish core of theory and praxis inherited from the rabbis of the Talmud and the Geonim, and, as Rambam and his son would have it, ultimately from the nebiim.