This is a fascinating question and while I wouldn't characterize it as an "evil stepmother" trope, powerful women at the imperial court were often judged based on whether they accumulated power at the expense of the imperial clan. Figures like Empress Lü and the much-later Empress Wu were often demonized, largely for misogynistic reasons but also because of perceptions that they sought to supplant the imperial (male) line by helping their own patrilineal clans succeed to the throne.

Later in the Han dynasty (depending on what scholarship you follow, either the reign of Han Wudi or the reigns of Han Xuandi and Yuandi) Confucian scholar-bureaucrats became a dominant presence at court. The degree of their power waxed and waned over the centuries but they remained the most potent force in intellectual life (including historiography) and a key force in practical court politics until the early 1900s.

While the institution of an Empress Dowager was very important in imperial China, and often relied upon to facilitate the imperial succession, the Confucian scholar-bureaucrat approach was otherwise a highly male-centric philosophy of governance. Women who sought to monopolize power from an Empress, Empress Dowager, or Grand Empress Dowager role were treated unkindly in the official histories. (Note that the "Empress Dowager" denoted the reigning emperor's "formal" mother, not always the same person as the biological mother, which sets this aside from the wicked stepmother trope). Empresses who seemed to display greater loyalty to their birth clans than to the imperial family were in for particular scorn for meddling with what was perceived to be the proper succession.

Empress Lü was (perhaps correctly) accused of placing the Lü clan in an advantageous position vis-a-vis the throne. She, of course, has been demonized in history. Compare her with Empress Deng Sui, who for all intents and purposes was sole ruler of the Eastern Han dynasty while serving as regent for her stepson Emperor Ai. Interestingly, she was extremely careful to avoid any appearance of favoring her family and made no effort to wrest power from the Han imperial line. While her brothers did serve at court, they were not given positions of exceptional power and were easily purged following her death. Of note, the official histories treated Deng Sui fairly well, going to great lengths to portray her as a studious child with a demure and forgiving personality - in other words, not someone who was a threat to the traditional power structure, even though she rose to its de facto highest position.

As another point of comparison, you can look at Empress Dowager Wang Zhengjun. She came in for mixed reviews from Confucian historians, largely because she showed loyalty to the Western Han imperial family (a plus) but granted real power to her relations (a big minus), ultimately giving her nephew Wang Mang the platform he needed to usurp the throne.

You can trace a similar evaluation line through other dynasties dominated by Confucian scholar-officials. Empress Wu Zetian was often demonized for giving her Wu clansmen a fighting chance at the throne after she usurped the formal title of Emperor from her sons and interrupted the Tang dynasty. The Song dynasty's Empress Liu, on the other hand, who much like Deng Sui dominated court affairs during the minority of her son Emperor Renzong, came in for mixed reviews. She was considered a competent ruler but faulted for investing her blood relatives with power above their abilities.

So ultimately, in addition to the blatant misogyny inherent to depictions of Empress Lü and Empress Wu, one of the dominant tropes at play here was of a female ruler more invested in her own family than in the one she married into, even at the expense of her children.

As for a "wicked stepmother" trope, perhaps the closest example would be Empress Jia Nanfeng of Western Jin, widely faulted in traditional histories for helping to install her disabled husband on the throne. Interestingly (and quite misogynistically, given that the men who ousted and came after her were equally and perhaps more to blame), Empress Jia is often blamed for the extreme chaos that followed her overthrow and execution. Of note, this reputation exists even though her period of rulership itself was competent, stable, and oversaw something of an intellectual renaissance in the capital of Luoyang. But one of the greatest charges used to tar Empress Jia's reputation was the fact that she was egged into having her stepson, the Crown Prince, killed. Indeed, the imperial relative who incited her into this action then used it to justify overthrowing Empress Jia and seizing the throne himself, precipitating civil wars that weakened the dynasty and facilitated its overthrow.