Canonically, in Shurima language, Sai, as in Rek'Sai means "desert". This is indeed a (near-)homonym of Turkic saï, yet the Turkic word means only a sub-type of desert surfaces, namely "desert pavement", not any kind of barren wastelands in general, like Shuriman Sai. So, it's likely that Sai is a native Shuriman word for desert & resemblance to Turkic saï is purely coincidental.
The full name of the great Shurima desert is Sai Kahleek. Kahleek sounds, perhaps coincidentally also like Arabic خَـٰلِقُ ḵaliq, which mean "creator" (albeit masculine; feminine "creatrix" would've been ḵaliqa(t)). It shan't take much of a stretch to to leap, meaning-wise, from "creatrix" to "mother" (just like "provider ~ protector" > "father" in Proto-Indo-European).
Is it possible that the Shurimans, whose language is fictional, borrowed Kahleek from a subtrate language based on real-life Arabic (the Stone Mage's name Taliyah is definitely non-native & borrowed from a Hebrew-based substrate)? Or because "creatrix" is ḵaliqa(t) in Arabic, & it is very unlikely that the Shurimans had borrowed the incorrectly-gendered word if they intended the meaning "Creatrix~Mother Desert", Kahleek is actually just native Shuriman for "mother" after all?