Westerners hear of the great library of Alexandria, or great centers of learning in Islamic Cordoba, Baghdad, or various places in Persia, but there isn’t a lot out there (in English, anyway), about great libraries of ancient or medieval China, Korea, Japan, Dai Viet, etc. There’s the tradition that Shi Huang Di destroyed all books, or all of certain books, which, given the presumed difficulty of such a task, seems to imply a degree of centralization, but on the other hand, Qin-era China seems like it might have had the sophistication of organization to go door-to-door to collect books from individual homes.
The point is, were there ever any great libraries of Chinese works and Chinese translations of foreign works?
There were major libraries and formal centers of learning in the Sinosphere, dating back at least to the Western Zhou period when texts and records were first put down on wooden or bamboo slips. As larger states emerged during the Eastern Zhou, their royal centers became focal points for scholarship. The most important of these was the Jixia Academy, which was maintained in the capital of the wealthy state of Qi with royal patronage. This was a place where scholars and philosophers were invited to take up residence, and their works were compiled and copied. This was during the era of the so-called Hundred Schools of Thought, and the Jixia Academy was among the most important centers of exchange and contact between these schools.
The idea of Qin Shihuang suppressing philosophers in general, and Confucians in particular, became a trope of Confucian writing in later periods but it's not clear exactly what was destroyed, in what quantities, or why. Whatever he did clearly didn't stop a huge body of classical writings from passing on to the Han dynasty, when intense study of these writings was considered a prerequisite for high office. In Han times, the imperial capital Chang'an was the site for a massive central library as well as an academy that trained scholar-officials for government service, with an enrollment that swelled into the tens of thousands during the Eastern Han. Meanwhile private schools for the sons of well-off families sprung up across the country, and bookselling was the only commercial activity considered "respectable" enough for a scholar.
The growth of Buddhist and Daoist monastic centers from the Northern and Southern Dynasties period onward introduced a new type of library, as prestigious temples sought to acquire more copies of religious writings. For Buddhist laypeople, paying for the copying or, even better, translation of sutras was a way to accumulate merit and show their devotion to the Buddhist community. This model spread to Korea, Vietnam, and Japan alongside Buddhism, leading to famous works like the Tripitaka Koreana, a complete edition of the Pali Canon compiled by the Goryeo kingdom in Korea.