Anita J. answered 12/18/19
Persian Teacher & Material Writer/International Translator/Interpreter
From the books I used to read in the past about the use of Borax in beauty products, I learned that--and I confirmed after reading your post--that Borax is, most probably, originally from Latin, brought into French, and eventually English. The synonym for Borax, which is Tankaar is the one with a Persian root.
Also, as far as I know, one of the meanings of the word "būrak", in old Persian, is the mold on the bread, which is very different from the anti-fungal property of borax.
I am not sure if you read Persian or not, but these websites might help:
https://www.vajehyab.com/?q=%D8%AA%D9%86%DA%A9%D8%A7%D8%B1&d=en
https://en.wikipedia.org/wiki/Borax
Best,
Anita