Where does “さい” come from?

さい (Middle Chinese) comes from Japanese 左様, from Japanese 様, from Middle Chinese 樣.

Ancestry of “さい”, step by step

Step	Language	Word	Meaning
1	Japanese	左様	like that
2	Japanese	様	way, style, appearance; be like, look like, seem...
3	Middle Chinese	樣	—

さい — Etymology, Origin & Word History | Etymology Explorer