Hi, sorry for taking some time on this, I've been busy irl and with other posts here.

You're right, chairs don't appear to be very common in China before this period. However, they were probably introduced earlier, in the Six Dynasties period, or as native developments from the Han dynasty. In "The Impact of Buddhism on Chinese Material Culture", John Kieschnik gives a couple of possible origin points for the chair in China:

The first is an indigenous origin: various low tables, armrests, raised platforms, and so on were common in aristocratic households in the late Han. Some of the raised platforms were quite similar to chairs in their use: they were sized for single people, and could be stored when not in use. It's possible these independently evolved into chairs.

The second is from a 胡床 huchuang (literally something like barbarian seat), a type of folding chair or stool. As the name suggests, they came from outside of China: originating in Egypt and spreading across Central Asia and into China during the Han dynasty, where the court, apparently enjoying various exotic foreign things started using them.

The third is the "Nestorian Hypothesis", where a handful of Nestorian Christian craftsmen introduced the technological techniques sometime in the seventh century.

Finally, there's the hypothesis that chairs were introduced through Buddhism in the Six Dynasties period, and by the mid Tang started to spread from there throughout Chinese society. Chairs were quite common in Buddhist temples in India, and were used in India as early as 200 BC. This hypothesis holds that chairs were introduced ultimately from India, through Central Asia, to China during this time.

He considers the last hypothesis to be the most likely origin point. That Chinese craftsmen were making various chair like objects, from huchuang to movable raised platforms, and so on, suggests they already had the technology to make chairs well before the Nestorian hypothesis has the technology being introduced. Various Chinese writers, writing from the Song and Ming dynasties, made similar observations that the by then very common chair wasn't present in Han and pre-Han periouds, and when trying to trace it's origin argued that the huchuang, while maybe leading to other types of folding chairs, apparently had no direct connection with fixed chairs, nor did the other Han dynasty chair like objects.

Instead, the earliest depictions of true chairs all seem to be in Buddhist contexts: certain Buddhas, such as the Maitreya, were commonly show in Chinese art from the 400s on sitting in chairs, and corded-chairs appear in translation of Buddhist works at this time. The earliest depictions of chairs in Chinese contexts also come from around the fall of the Northern Wei, starting on a stele around 535. This and the next representations we have over the ensuing decades are all in Buddhist contexts, with monks sitting and meditating on corded-chairs, just as in India. Even in the early Tang, textual evidence also strongly associates chairs with Buddhism. This includes a monk, Yijing, complaining that monks don't sit in chairs properly when compared with proper Indian monks, and noting that chairs were probably introduced into monasteries around the third century, as well as various documents talking about officials visiting monasteries and being seated in chairs.

Unfortunately, how this spread to society as a whole is unclear. Kieschnik thinks the court may have played some role in popularizing them, but thinks in a highly religious time, lay people visiting temples would have naturally wanted to copy the environment there. Ironically, after they spread the original Buddhist associations were kind of forgotten, and the connection between chairs and religion lost to the point where people were complaining about chairs being a symbol of spiritually decayed and corrupted lay life.

I think Kieschnik makes a strong case that this is where they came from, and that the Nestorian hypothesis is almost certainly wrong. There is still a chance that the other two hypothesis are correct, though less likely, but the timeline looks somewhat similar with much earlier origins, then spreading during the Tang dynasty.