Al-Jazari's knowledge seems to have ultimately derived from a Baghdad library, via the Banu Musa brothers.
I find the history of those libraries fascinating https://en.m.wikipedia.org/wiki/House_of_Wisdom.
Kinda OT.
Apparently he was a Yazidi Kurd; that's what the circumstantial evidence shows, and there's no other evidence AFAICT.
It says "Muslim engineer", which would be like saying Steve Jobs was a "Christian Engineer".