The part where it said they didn't know face powder was poisonous was believable, as science was practically zero back then. I've seen several Chinese and Korean period dramas address that.
What confused me is how she ended up as a a servant in the palace. Oh, and btw, don't call her slaves because servants and maids do get payment and for many families from poor background. AFAIK, it was a privilege to have daughters serving in the palace.
What I don't understand is that young, unmarried, physically fit girls usually have to go through many rounds of selection process. The selection criteria varied from emperors to emperors, but I don't think they would accept someone from a red light district, unless her kidnappers gave her a new identity. You can read more about the selection process here: https://multimedia.scmp.com/culture/article/2154046/forbidden-city/life/chapter_01.html.