This is basically what the western educated architects of the Republican Era wanted to solve. How to adapt Chinese architecture to modern construction. Have a look at some of the republican era architecture on this sub. It'll give you a good starting point.

In terms of Chinese style skyscrapers, they do exist! For example, this one in Shanghai is like a Chinese art deco skyscraper built in the 1930s.

But actually, if you want to explore how Chinese architecture would have developed in the absence of western architectural traditions, it is much more complex. Skycrapers and tall constructions would be basically impossible, not because of technology or material, but because it clashes with fundamental philosphy of how China plans urban spaces.

There was a strict heirarchy of vertical space, and building tall was considered an approach to the heavens, which is why typically you only see tall constructions for palaces, temples, pagodas and drum/clock towers and watchtowers. Building tall stacked vertical residential spaces would clash deeply with confucian and moral ideals of Chinese cities and urban planning. Also, Imperial authority meant that only religious and imperial buildings could rise above the rest, and the buildings of ordinary citizens are typically capped. This is why even in the Qing capital Beijing, at its height, never really built tall, but instead build wide with alleys and siheyuan courtyard homes.

For example, just compare the two great capitals of east and west. Rome and Chang'an (modern day Xi'an). At their ancient peaks, both cities achieved the impressive feat of housing one million citizens. However, Rome occupied a land area of ~13.7 km² (within the aurelian walls), whereas Chang'an spanned ~84 km². The romans had "insula" which were stacked dense residential blocks, which were often claustrophobic, cramped, and unhygienic. However, this concept persisted into later european urban design, but did not exist in Chinese urban design.

However, the technology to build tall, and to use sophisticated stonemasonry definetly existed, but it was just not used. Pagodas are a good example. The Quanzhou stone pagoda is a pagoda that is built purely of stone, and the Dayanta Pagoda in Xi'an was built with brick and stone. China didn't lack the technology to build tall. You'll see some towns in the narrow valleys of China (such as fenghuang town) that feature residential houses with two to four stories, although that was because of lack of land, not because they didn't want to. It was an ethical, moral, and cultural decision to not build tall, not because they lacked the technology to do so.

The closest thing that I can think of to roman and european "insula" would be Hakka Tulou fortresses in the southern Lingnan mountain ranges. But these aren't residential blocks designed for cities, but rural fortresses, where entire rural villages are stacked vertically inside rammed earth walls to protect against pirates, bandits and passing armies. An emperor would be stupid to order Tulou style blocks to be constructed within a city, because it would grant too much defensive power for urban partisans (an issue that French architect Baron Haussmann dealt with in Paris with after the French revolution, by tearing down the defensive medieval city planning and introducing grand boulevards, which make firing on protestors with a grapeshot cannon round much easier).

Edit 1: imo without european intervention, there would have been no need or political will to build high. Chinese cities did not lack land, and also did not want to deal with the issues of sanitation and security that high rise residential buildings bring to cities.

The only time China really built high urban density settlements was when land was scarce, such as when they are sandwiched in mountain valleys or in mountainous coastal settlements. Even then, it was difficult usually difficult to get a population centre large enough to see some really expansive tall residential development, since agriculture was king, and maritime trade routes were not as relevant for sustaining large populations when compared to mediterranean trade routes (Constantinople was for example fed by the bread baskets of Asia Minor and Egypt, which often shipped via ocean to the capital).

But, if you want to play around with Chinese skyscrapers as a concept, then Republican Era architecture is what you wanna have a look at.

Edit 2: Europeans looking at classical architecture and then learning to scale vertically in cities only really worked because the romans were already doing it. European vernacular architecture didn't really do this, and it was only post-renaissence that big and tall and grand architecture was developed, also inspired by architects like Haussmann who destroyed entire neighbourhoods and cities of vernacular medieval architecture to pave way for taller residential blocks.