I've gone on to mention these in other posts, but there were historians from all over the world in ancient times. And they could be just as reliable and unreliable as Greco-Roman historians, in fact, Greco-Roman historians like Suetonius are notoriously unreliable for the inaccurate and often satirical pictures they portray of figures whom they disliked, or depending on which person ruled at the time at which they lived (since one could end up with their head on a spike for saying the wrong things). In reality, "accuracy" also depends on the modern scholar and how they interpret the work. Modern historians function under a background of methodological naturalism, which did not exist among ancients, and so any attempts at using their work to reconstruct the past is a game of probabilities (and sometimes a fair amount of educated guessing).

As for ancient historians who were not specifically Greco-Roman, here are some I am aware of from around the first century CE:

Josephus was a Jewish historian of ancient Palestine, and is our most reliable (mostly because he is our only) historian of the region for the first century CE. Pamphile of Epidaurus was an Egyptian historian (and a woman too!) who was frequently cited by her contemporaries as a reliable source of information. Unfortunately her work is lost. She was of Egyptian descent. In China, there were a few as well: Ban Zhao, Ban Biao, and Liu Xin, who all come to mind.

One of the most necessary scholars to know is Isidore of Seville, who is often considered the "last scholar of the ancient world". He was Spanish of Hispano-Roman descent, and he was writing under the rulership of the Visigothic kings, and provides us with some of the only information we have on the Goths a viewpoint that was not specifically from their opposition (Jordanes and Procopius both being on the Roman side of the equation).

Anyways, long story short, these historians are all worth exploring and all of them recorded histories just as the Greco-Roman historians did, and they are comparably reliable or unreliable, just as the Greco-Roman historians were, by modern elitist standards of "history."

I don't know enough about Greek and Roman historians to attempt comparisons but Ancient China had plenty of historians, Sima Qian of the early Han and his Records of the Grand Historians who was held up as an inspiration (or held as a warning) by history during the latter Han's collapse. There was the Latter Han era Ban siblings, Ban Gu dying in disgrace so his sister Ban Zhao took over, writings on the history of the Early Han. The Latter Han ever now and again would see Emperors or controllers decide their dynasty history needed updating with leading scholars of the day like Cai Yong, Ma Midi, Yang Biao, Cui Shi, Zhu Mu, Ban siblings, Ma brothers.

In my era of interest (190-284 CE), there were historians like Ying Shao who, seeing the Han collapse, wrote of the rituals of the Han from notes and memories, wrote of customs and legends and compiled legal decisions, his work remains an important source of information on the later Han. Men like the soothsayer Qiao Zhou began developing works of local history, others wrote about their family like Zhong Hui about his mother.

The main figure of history was Chen Shou from Yi province, who served in Shu-Han's record office than when the state surrendered to Wei (which quickly became Jin), would serve there. Among his historical works, he compiled the records from each kingdom (Wei, Wu and Shu-Han) into one history work as a private project. When the work was published, Xiahou Zhan burnt his work since it couldn't compare and it is held in good regard with Chen Shou seen as fairly neutral under the circumstances

Liu Song scholar Pei Songzhi would gather up other sources like the figures I listed above to include as annotations to supplement Chen Shou's work and to fill in holes. Including the regicide that Chen Shou was not able to include at the time. Pei Songzhi included figures of the era like Wang Can a scholar of Liu Biao in Jing then of Wei dynasty, Wei scholar Yu Huan who wrote a history of Han and history of Wei (his interest in lands abroad help us understand attitudes of the time), the seemingly well connected Wu scholar Hu Zhong. Works from the histories compiled by Wei and Wu dynasties, letters and memorials that survived, ghost stories, works and commentaries about the three kingdoms from those that came after like Sun Sheng.

Ancient Chinese history could be private works from a scholar or a sponsored work by the government or a government charged work with a panel of scholars, in some cases using life experience and those they know but also access to the imperial records. The quality would depend on the scholar, bias could reflect their home pride, their gentry background and political pressures of the day. There are inaccuracies in the texts, there biases of their background that modern historians attempt to counter (hello gentry vs eunuchs) or personal/political bias of their situation, some bad work, some fantastical mystical stories. Alas, they insisted on using humans to write their histories so perhaps not a surprise those issues crop up.

But for all the issues in Chen Shou's work, it is a reliable source led by a well-regarded historian and supplemented by the work of scholars during that time and since. Ying Shao's work remains of importance for understanding the Latter Han and there were other scholars of note who helped improve our understanding of their time or what had gone on before.