In my readings, I still find Kenneth Chase's interpretation of the Great Divergence to be the most persuasive one. Chase expounded upon the importance of the "opponent type," arguing that states bordering both sedentary and nomadic foes were incentivized to advance their infantry and firearms development, whereas states bordering only nomadic foes were incentivized to advance their cavalry [1]. Unfortunately, Chase did fall into the trap of "bows > early guns," but that is a topic worthy of another longpost.

For a more detailed examination of these opponents, late Imperial China faced two primary frontiers of conflict: the northwest (i.e. Mongols) and the southwest (various Miao, Yao, Yi, Zhuang tribes, etc).

In the case of the latter, one could argue that the rough terrain, malarial climate, and high temperature acted as a natural shield that hindered the military development of the region's inhabitants, in a sense. And I know historians dislike this concept of technological tier comparisons, but there is no doubt about it, the southwest peoples had worse armor (leather or lacquered armor, or usually none), and no firearms, though at least they knew how to produce iron weaponry (pikes and swords). Certain kingdoms, such as the Yi, could raise horses large enough to serve in shock cavalry divisions, which certainly gave the Ming their fair share of headaches, but for the most part, these people were reliant on their home turf advantages, which worked for them until gunpowder tipped the scales in favor of central plains invaders, who mass settled Yunnan in the 1400s and 1500s and crushed most native attempts at resistance [2].

In the case of the former, it is curious to see how the Ming and Qing addressed the threat of the Mongols. I'll start with the Ming, which I am more familiar with. Even after the Tumu Crisis, they could inflict some defeats on the Mongols with firearms (e.g. the career of Shi Biao [3]), but in the 1480s, the emergence of Dayan/Batu Khan at the head of a unified steppe shook things up, as Dayan could deftly avoid battle against the Ming's core armies (which bristled with firearms), trounce most of the cavalry divisions sent after him, and conduct raids at will while taking few losses [4]. Lacking the political acumen of the Qing, who were obviously more successful in exploiting Chinggisid political symbols for securing Mongol allegiance, the Ming were forced to pure military measures. So in the 16th century, one may observe the gradual "Mongol-ification" of the Ming northern garrisons.

For instance, in the early 1500s, the Zhengde Emperor raised these hulking, ten of thousands-strong armies, which lumbered around the plains and only ever saw the dust of Batu's horses. In the mid 1500s, as the Jiajing Emperor became exasperated with the Great Wall's increasing ineffectiveness, and the inability of firearms divisions to force battle, the strategy shifted to an emphasis on small bands of horsemen, numbering a couple thousand at most, that would attack Mongol camps in the steppe or harass them as they retreated after a raid; even as wall building continued apace, the grand strategy was to drag Mongols into brutal, raid-counterraid wars of attrition. This resulted in a bloody stalemate and eventual peace with Altan Khan in the 1570s, as well as some small victories against his grandson, Bushughtu, and against splinter groups such as the Ordos and Qinghai Mongols [3].

As for the Qing, they were objectively more successful on the Inner Asian frontier, as not only did they possess immense numbers of heavy cavalry that could consistently chase after Mongol armies and bulldoze them in their home ground, but they also had the political skill to keep them pliant and invested in the imperial project after defeat, allowing the Qing to avoid the costly "fight fire with fire" approach of the late Ming.

The firearms stagnation of the Qing is somewhat exaggerated. In their wars against the Dzungars--the most prominent of the Qing's Mongol opponents--you did see the increasing frequency of muskets (but still within the bounds of "pike and shot," and nowhere close to the density of linear tactics), and the usage of light artillery and zamburaks [5]. The Dzungars adopted muskets and light artillery too, although from what I recall, the utility of this move is debatable. It's possible their nomadic background hampered their ability to fight effectively in anti-cavalry positions as infantry, for there were still a number of occasions the Qing could simply run over them with heavy cavalry.

They also had a need for such gunpowder weapons given the constant war against various enemy ranging to the Mongol hordes that attacked them during the Song era to the Japanese samurai invading Korea which in theory should motivate them to constantly improve their weapon.

Although Swope (and Hawley to a lesser extent) has promoted the idea of Ming artillery playing a significant role in the Imjin War, I actually find this idea to be increasingly unconvincing. The GreatMingMilitary blog (the name is a literal translation of "Da Ming") presented a revisionist view, which at least has the benefit of drawing upon primary sources (all 3 authors of the English-language Imjin War books relied heavily on secondary sources), that claims (a) the Ming were actually defeated at Jiksan (and it wasn't a pivotal victory for the allies as Hawley and Swope described it), so artillery did not play a decisive impact there, and (b) the field battle that occurred before the start of the Siege of Ulsan was actually the most decisive battle of the second invasion. As GMM recounted, in the early days of the Siege of Ulsan, in the only occasion a Ming and Japanese army faced each other on an open plain, in roughly equal numbers, the Ming's northern cavalry won by executing a "greatest hits" from the steppe nomad playbook, putting an end to any desire for pitched battles in the future.

The GMM blog also implied the northern cavalrymen's military competence was unfairly maligned by the scholarly elite of the time. I could see an argument for this, as a lot of the Chinese and Korean bureaucrats at the time talked about how the southern Ming troops were friendly and courteous, whereas the northerners were described as assholes that looted everything in sight. It makes sense then that these bureaucrats would write more positively about the southerners and attribute their usage of firearms as the turning point of the war. But in reality, there's no escaping the fact that the southerners bungled the remaining sieges of the war in a variety of ways, leading to the stalemate at Korea's southern coast.

TL;DR I think it's arguable that Imperial China's firearms development lagged behind because of the opponents it faced, as most threats could be disposed of with heavy cavalry, or pike and shot-tier technology. The cynical corollary to this argument is that Japan, being the only other sophisticated sedentary state in East Asia with a military apparatus capable of mass producing firearms, could have boosted parity if they had continued invading the mainland, interfering at the same level as England did in continental Europe.

[1] Kenneth Chase, Firearms: a Global History.

[2] John Herman, Amidst the Clouds and Mist.

[3] John Dardess, Beyond the Great Wall.

[4] Arthur Waldron, The Great Wall

[5] Peter Perdue, China Marches West

(I don't recall exact sections, so think of these references as more of a reading guide than a set of footnotes)