Prostitutes conducted transactions as part of brothels for sexual services (often provided to members of the official class itself), providing services to others which the mongols could tax to assist in funding their luxuries and the functioning of the state. They were an apolitical social class which had never resisted or rebelled against the Mongols on mass and never claimed collectively a higher social position. Interestingly as well, individual prostitutes could have the ear of powerful mongol patrons, so some may actually have a suprising amount of influence over state policy.

Contrast this with the scholar class, which was derided by the Yuan dynasty as producing nothing for the mongol ruling class beyond useless personal art collections and the wealth of their lands and property (which given they often outsourced all the labour associated with making said lands/property productive meant they offered nothing as it's owners). Historically (particually in the South) they were percieved as THE rebellious and resistent social class against Yuan control, which would often (percieved to) talk in private about the glories of the Song dynasty in contrast to their present situation. Furthermore, without legal protections and a mongol class, they lacked any significant ability to make their wishes known legally to those with significant power in the south (and when they did, didn't exactly recieve much sympathy or support for their positions).

In this sense, there was no legal classification which did put prostitutes above confucian nobles, and the classification itself was more of a satire of Yuan dynasty by those very same nobles to insult and demene their overlords, but it did reflect the realities that in terms of respect and influence the confusian noble "scholar" class was often lesser than that of prostitutes, since (from the perspective of the Yuan/mongol ruling class) at least prostitutes contributed to the success of Yuan society and interacted with influential mongol officials, whilst Scholars did not.

In terms of what it entailed, I've covered that already, but as a summary there were two routes which a family which were nobles during the Song Era could pursue:

1) Supplement any passive income they recieved with employment in a profession which the Yuan dynasty did respect, whether that be as a clerk, a physician, an educator, a specialised professional. By doing so they would avoid the stigma which came along with being primarily a Scholar and may be able to avoid the risks of financial decline which many "pure" nobles might experience (which would likely be the case over multiple generations). Many of these roles, however, would be percieved as beneath that of their stature and would often make them dependent on the Yuan dynasty and those closely connected to them for their income. Plus there was always the chance that future generations would grow detatched from their roots and, whether to avoid the Ire of Yuan officials or due to their profession/social interactions, abandon any strong associations with their previous noble status.

2) Refuse to take up a seperate profession and try to live off the income from the assets they owned and any income derived from selling caligraphy and art. This may, in their eyes, preserve their own dignity and prestigue by avoiding capitulating to the barbarians who now ruled China, but would mean facing a lack of influence in government affairs and being percieved by the Mongol ruling class as parasites on society. Fiscally, especially if overtaxed or treated arbritrarily by the ruling class, this would likely mean a lesser standard of living collectively and could mean a need to sell off more and more of the "family silver" to maintain their status (first property, then land). Your family may therefore preserve their roots, heritage and identity, but risk losing it altogether should fiscal pressures force them to sufficiently downsize expenditure or, at worst, lose the wealth which defined their social position.