For China, the obvious recommendation is Joseph Needham's Science and Civilisation in China, Cambridge University Press. This is a not-for-the-faint-of-heart monumental multi-volume series, with the first volume published in 1954, and now with 25 of 27 planned volumes published. For something shorter, Robert K. G. Temple, The Genius of China: 3,000 Years of Science, Discovery, and Invention (originally published 1986, and reprinted by multiple publishers and easy to find second-hand) is a one-volume summary for the general reader, and Colin Ronan (1980–95), The Shorter Science and Civilisation, Cambridge University Press is a 5 volume summary. One strength of SCC is that it gives translations of primary sources otherwise unavailable to those who don't read classical Chinese.

For a recent history of science and technology in China, Yongxiang Lu (ed), A History of Chinese Science and Technology, Springer, 2015, covers similar ground in 3 volumes.

Of all of these, Temple is the best short work for the general reader (because the others are multi-volume works aimed at more specialised audiences). Individual volumes of Needham's full work are IMO accessible to the interested general reader; for a list of the volumes, see https://en.wikipedia.org/wiki/Science_and_Civilisation_in_China

For Indian science and technology, there are two major multi-volume works, both published in India, and neither of which appears easy to find: the older is O. P. Jaggi (ed), History of Science and Technology in India AKA History of science, technology, and medicine in India, Atma Ram, published 1969-1986 (15 volumes), and the newer is G. Kuppuram, K. Kumudamani (eds), History of Science and Technology in India, Sundeep Prakashan, 1990 (12 volumes). I've read neither, but it could be worth checking if either is available in a nearby university library.

For a one-volume work, there is by D. M. Bose, S. N. Sen, B. V. Subbarayappa (eds), A Concise History of Science in India, Indian National Science Academy, 1971. I've not read this, but have briefly skimmed through it and it seems OK.

Relatively little has been published on pre-Medieval Central Asian and Middle Eastern science and technology. Central Asian and Middle Eastern science and technology largely deals with science and technology after the Islamic conquests, and neglects the preceding Central Asian science and technology that the Islamic Golden Age of science built on. Alas, I have nothing to recommend here (but am interested in any recommendations from others).

Of the Golden Age books, if you're interested in recommendations, I'd suggest starting with Al-Khalili, Jim (2011), The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance, New York: Penguin Press.

Helaine Selin (ed), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, 3rd ed, Springer, 2016 has lots of good stuff. If it's available via a local university, it's worth checking.