In terms of direct power, it varied. Anything the emperor decreed was supposed to be treated as a sacred edict, and many dynasties worked to create strong central governments with local rule delegated to local officials. Some emperors, like Ming Taizu acted with extreme vigor and despotism, overseeing many aspects of his empire and very much exercising direct rule over his officials and subjects. This power was further strengthened by the enfeoffment of royal family members as powerful 'feudal' lords.

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In theory, the emperor held absolute power. To break it down barney-style because this is reddit: the emperor of China was in theory the sole legitimate ruler of all China and was therefore the acting son of heaven (Tianzi), and he acted through the mandate of Heaven (Tianming), which granted him rule over all subjects under heaven (Tianxia). As sole legitimate ruler and the earthly representative of heaven therefore, the emperor was given the freedom to do as he pleased. He was under no legal obligations but the very rigid Confucian education that the royal princes of Imperial China would have received still would have given him a strong moral framework by which to organize his rule, in theory.

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In practice, the power of the Chinese sovereign has swayed dramatically. The Chinese emperor was never fully reduced to the role of a figurehead for the 2,000+ year Imperial history of China, but there were definitely emperors who saw their power wane as external actors infiltrated their court. At least one emperor, Emperor Tianqi of Ming was completely illiterate due to probable mental illness and as a result, the many court eunuchs seized power in the Ming court, which was disastrous for the late Ming. The Tianqi emperor was largely uninterested in court affairs, and many of the official, 'royal' decrees were actually the work of eunuch Wei Zhongxian. Wei and some other Ming courtiers basically seized control of the government with Wei operating as the de facto head of state, and the Tianqi emperor was left powerless. Generally, gross negligence was probably the biggest reason why many Chinese emperors lost control of their government and people. Examples include the Wanli emperor of the Ming, the late reign of Tang Xuanzong in the 8th century, Song Huizong, and so on. In many of these such cases were the emperor was willfully or otherwise neglectful of his duties, ceding power to officials, and as a result, corruption flooded the already corruption-prone bureaucracy and court of Imperial China. Factionalism and other fun consequences of governmental dysfunction took hold, and in some cases threatened to destroy the dynasty.

Another perspective into the power of the emperor is looking at the instances in Chinese history where there were competing regimes. During the Song, there were two such competing powers in China. The Song was reduced to a rump state in 1127, and the Song competed for power directly with the Jurchen Jin dynasty to the north, meaning that the Song emperor didn't exercise any sovereignty over the northern Chinese population despite his claim of being emperor of China. So in this case, the emperor didn't exercise absolute power over all of China either.

Thirdly, when an emperor was too young to rule, or when there was a retired emperor (Taishang Huang), the sitting emperor was also usually hobbled in their ability to dispense their power. In the case of a child emperor like the first few years of the Kangxi emperor's reign for instance, the power of the emperor would be delegated to a regent. The reason for why this was the case should be... readily apparent. For retired emperors, filial piety and some other reasons usually meant that de facto power was still in the hands of the older emperor. The retired emperor's edicts would, for instance, carry more weight when addressing political issues. The retired emperor could also just straight-up overrule the reigning emperor. This was the case during the era of the An Lushan rebellion, when retired emperor Tang Xuanzong made several military decisions without consulting the reigning emperor, Tang Suzong.

But on the other hand, when China had a capable ruler, his rule was definitely absolute. China has always had a knack for despots, whose rule were sometimes equal parts brilliant and terrifying. The first and third Ming emperors were notorious for both their vigor and despotism, and many of the dynasties in Chinese history relied upon strong men to solidify rule over China. But rarely did these eras of efficient and strong rule last for long, and the 'tone' of an emperor's rule could change dramatically throughout the lifetimes of even the emperor's life, his power waxing and waning as a consequence.