Nice question! Just a note, I’m not aware of such anime (?) so I am just basing this response on information given above and otherwise don’t know the situation. So anything further please consider this. Also I am going to focus on prostitution, but know that this also extends to labor.

Tl;dr: Women and children were more or less considered property as legal status, but this is still somewhat simplified to be fair. Toyotomi banned international slave trade and chattel slavery. He was more concerned about involuntary servitude so no kidnapping and slave trading. So voluntary servitude might be ‘slavery‘ by definition, but this was not necessarily interpreted this way. The objective of Toyotomi and subsequent Tokugawa shogunates was for political stability and it appears that it wasn’t necessarily without exceptions or paradoxes. The ‘government’ cared, but not for the reasons one might assume in a sort of ironic way so they ended up allowing these practices.

So this arrangement is often called ‘voluntary indentured servitude’, or using debt as means for servitude. So this might not be ‘chattel slavery’ by definition, but it could be a form of slavery. (I might switch terminology a lot.) Variations of such types of labor arrangements appeared in other places like the first settler colony of Jamestown. Essentially a family can use a person’s (child’s or wife’s) labor for credit from a third party ‘employer’. The payments to loanee varied depending on work, but think of it like financing in the multiple ways this can be done. So this might be a general model. Then in contract the employer applies the loan as debt to the indentured person. This could be managed in a number ways such as ‘adopting’ or ‘apprenticing’. So legality is even trickier as there were ways to get around depending, but there wasn’t really any labeling of ‘slaves’. Often also these contracts might be verbal. The debtor can supposedly work it off or be released after a time period. The loanee can also pay the debt, but it is essentially buying back the person because of interest, gained skills, or including welfare (ie shelter, food, etc). There is also where a person becomes collateral if the loan defaults. There were various policies throughout Japanese history governing how these contracts worked. Often there were time limitations from a minimal several years up to a maximum of ten years such that servitude for a lifetime was not allowed in some periods. There were also like an employment-like arrangements. However there is evidence that there were suspensions of these edicts during bad economic times (ie famines, disasters, mass migrations) and modifications during good times. So unfortunately lifetime servitude might not have been rare. More later.

So Hideyoshi Toyotomi never actually banned ‘slavery’. He in fact banned slave trade and Japan’s participation in international slave trade (人身売買 jinshinbaibai). Here is an excerpt from Boscaro’s study on copies of the Toyotomi edicts (originals are lost to time):

Because it is unlawful to sell Japanese people to Great China, to Southern barbarians [referring to Europeans] and to Korea, the selling and buying of men in Japan shall be prohibited (Boscaro, 1973)

The Portuguese were involved in buying and selling slaves throughout the world, and this appeared to be helped by the Jesuits to say the least. This was the beginning of the sakoku edicts (just generalizing the term here) and expelling the Portuguese and Christianity. See de Sousa (2017) for more information on Portuguese Slave Trade in Japan. So Toyotomi might have always been looking at things through a political lens. Toyotomi was also not without contradiction taking many Korean slaves in the Imjin War. So draining the Japanese peasant population (or his subjects) might have been a bigger concern as the Portuguese carted off Japanese slaves on their ships and often resold them elsewhere. Plus someone or an entity internally could amass too many slaves to challenge the regime. Also during the sengoku era agricultural output declined and became unstable, and thus created a plethora of problems and knock-on effects. Toyotomi and subsequently Tokugawa appeared to understand that stable agricultural production if controlled well would make the social and political conditions docile. So a peasant class was needed. This can only be deduced as there wasn’t much exact clarifying reasons given by Toyotomi and then the later Tokugawa shogunates in their edicts. Eventually chattel slavery became a rare institution and there was a shift to more ‘free’ labor within the caste system, but it existed with inconsistencies and paradoxes from a modern point of view. One article describes what Toyotomi did was banning “unfree” labor or involuntary servitude, but the definition of unfree is not assumed to be equivalent ‘free’ labor in the most ideal. So it doesn’t appear that the Tokugawa shoguns were willing to let exceptions happen as long as it did not upset their hegemony as they certainly had room for interpretation. This was still the age of might is right. There was also corvée labor and criminal servitude. There was also a caste of hereditary servitude, basically owning or beholding an entire lineage of people within a household. These servants were like a caste of their own. So I think it can be deduced that this was the far from the legal institutions of human rights, but not the same as the status of slaves in the American South. It was something in between.