I have a copy of Memoirs of a Geisha but I have never managed to read it. From what I understand from my husband who is of Japanese descent but who also lived in Japan, nowadays being a geisha is more of a choice than it was in the past. It is one heck of a lot of work to learn all of the skills needed in dance, music, conversation, poetry, demeanor, clothing, money management, and so on.
Modern Japanese women have a number of career choices available to them these days, so any that choose to become geishas must be very dedicated. Legitimate geisha are not sex workers. They are single and may choose to have a relationship with a client, but they are not required to do anything more than flirt. In Japan, men are amused by the illusion of that which is never to be, and the geisha is skilled in the art of making men feel desirable and witty without ever having to even touch the client.
From what I understand, there aren’t very many geisha anymore, only a few thousand. OTOH, there have always been and still are prostitutes in Japan, ranging from street walkers and bar girls on up to elegant escorts. But these women are not geisha.