A thing I often wonder when browsing “Rome (or any other large empire, really) Survives” threads is that surviving large empires might breed more stagnation in society compared to more Balkanized areas that are constantly in competition with each other (read: war). I have to wonder though: is that really true? A example given is Qing-Era China, though it must be noted that, in that society, the merchant class was heavily looked down upon. Commercial competition breeds just as much innovation as military competition does, if not more so, and so I am wondering, could commercial competition breed innovation and stave off stagnation in any other large, peaceful empire, or would such commercial competition even be present due to the nature of such empires?
Yes, but only in specific scenarios.
Innovation requires two things: motivation and material resources to be able to dedicate to innovation. Naturally, the existence of a competitor creates that motivation to innovate lest one falls behind their competition, but the state also needs to be stable enough to either directly or indirectly support innovation. As such, the competition needs to limited in scale enough that states are able to have the luxury of being able to spend money on long-term investments like research, researchers, and the adoption of new technologies.
As you point out, Qing China is an example of a state with the resources but without the motivation to innovate (in broad strokes; post-Taiping Qing lack both material and political capital to effectively reform and an argument could be made that the Manchu rulers didn't have the political capital with the Han to push for innovation or reform).
To contrast, there are also examples of states with the motivation but without the resources for innovation. The Sassanids for instance had been engaging in protracted warfare for centuries against the Byzantines that had weakened their empire and caused stagnation that eventually lead to their rapid downfall at the hands of the Rashidun Caliphate.
I believe Native North America was in a similar situation, where the 13th-14th century climate optimums caused instability that resulted in military developments such as longbows, improved armor, and advanced fortifications, but it also weakened and led to the collapse of societies like Cahokia, obviously reducing the Native American capability to innovate and adapt right before the European discovery of the Americas.
In this regard, Europe had an advantage in both having significant competition, but also being in a stable enough equilibrium where states had the relative freedom to innovate instead of merely worrying about their survival this year and reliable communication could still occur between states to form the likes of the Republic of Letters (for the most part, but even devastating wars like the 30 Years War or the Napoleonic Wars still had major belligerents effectively be untouched by conflict).
It saw a lot of philosophical innovation, certainly, though AFAIK it didn't see as much technological innovation. (Though I could very well be wrong about that -- I'm not an expert on the period.)
Off the top of my head, the Warring States saw the development of polearms and pikes, mass adoption of crossbows, the transition away from chariots to horse-riders, traction trebuchets/mangonels, the rise of large-scale infrastructure projects, and the final steps of the transition from bronzeworking to ironworking.
Edit: Also, continuous interstate competition/warfare also results in the development of an advanced commercial class, since states need to finance their wars somehow.