An old but thorough overview by Edwin Pulleyblank: https://doi.org/10.2307/3596015. This focuses on a later period but touches on the one in question: https://www.cambridge.org/core/books/abs/cambridge-world-history-of-slavery/slavery-in-medieval-china/DA418A6A4FCB777D652FF183EBBBFF10.

The concept of slavery in early imperial China (Qin and Han dynasties) was somewhat different, as you note, from chattel slavery practices in other societies. Generally speaking, only certain individuals were "supposed" to be enslaved (primarily as the result of military defeat or judicial punishment). But in the years prior to the reunification of the realm by the Qin and Han dynasties, practices more akin to chattel slavery became more common (kidnapping individuals to sell them into slavery, self-sale or the sale of children, and debt-related slavery) though never in such amounts as to become a dominant form of agrarian labor.

Also notably, only certain individuals were entitled to use enslaved labor (princes and government officials, and even then, only in apportioned numbers). In practice, by the time the Western Han dynasty met its demise in 9 CE, the official class was synonymous with landed gentry families that periodically married into the imperial clan and accumulated vast amounts of land and retainers, and significant numbers of enslaved people to serve within their estates. This gentry posed a direct threat to the emperor's authority and indeed, was primarily responsible for a sequence of regime change between 9 CE and 23 CE. Slavery abolition efforts during this era fit within this political context. As discussed above, the form of slavery practiced by this gentry had expanded beyond "traditional" conceptions in certain ancient Chinese moral/philosophical texts, such as the Book of Documents or the writings of Mencius, of slavery as a judicial punishment.

Wang Mang, whom you mention, was the most notable figure to promulgate the abolition of slavery in this era, albeit unsuccessfully. He was himself an imperial in-law and as such, belonged to a wealthy and powerful clan. He rose to power by 9 CE - first to a position equivalent to prime minister, then to "acting emperor," and finally to emperor - using a brand of ruthless political maneuvering blended with appeals to Confucian moral authority. Wang Mang was an erudite individual surrounded by conservative Confucian scholars, and they made creative use of archaic moral and historical texts to justify social reforms that served the dual purpose of disempowering the new emperor's political rivals.

In the case of slavery, Wang Mang used evidence from early Confucian texts (namely a line from the Book of Documents) to argue that non-judicial slavery was improper, thus justifying an abolition of slavery within the empire between 9 and 12 CE. Although the reform was strictly enforced, it engendered strong opposition and was never accepted, and like others of Wang Mang's reforms was withdrawn. Ultimately, the landed gentry that Wang Mang had sought to weaken played a major role in the rebellions that toppled his regime in 23 CE, and a landowning gentry leader with distant Han imperial relations, Liu Xiu, became the first emperor of Eastern Han.