This is a huge topic, with a lot of scholarship and debate within the historical academic community. So for China specifically (it’s a book about why Song dynasty China, despite having a lot of the preconditions for industrialization, didn’t industrialize), probably the best place to start is The Great Divergence: China, Europe, and the Making of the Modern World Economy by Kenneth Pomeranz. I don’t agree with all the conclusions of that monograph but it’s a great first foray into the questions and concerns of this kind of longue durée history. Adam Smith in Beijing: Lineages of the Twenty-First Century by Giovanni Arrighi makes this argument that the Chinese state was strong enough to stop capital from taking over and that the way capitalism formed in the West is actually rather odd; this is a wonderful book but it requires quite a bit of context, and you might even be better off starting with his more broad account of the rise of capitalism called The Long Twentieth Century: Money, Power and the Origins of Our Time, which (despite its name) covers around 500 years from the formation of capitalism in Renaissance Italy up to the modern era. Fernand Braudel’s three part Capitalism and Civilisation, from which Arrighi draws a lot of his ideas, is phenomenal but very long and again requires even more familiarity with the historical period.

If you just want a quick summary of all the above, distilled into something quite short but still well done, I’d recommend The Origins of Capitalism and the ‘Rise of the West’ by Eric Mielants. It’s not specifically focused on China, but it does cover the “capitalism requires the state” bit and why capitalism happens in Western Europe and not anywhere else. For some additional counterfactual history of why the West got rich and the East didn’t, I recommend ReORIENT: Global Economy in the Asian Age by Andre Gunder Frank and Fossil Capital: The Rise of Steam-Power and the Roots of Global Warming by Andreas Malm (this book in particular is important, since it doesn’t cover the larger question of why the West and not China, but it does push back and disprove a lot of Pomeranz’s points about coal power).

You can also check out The Origin of Capitalism: A Longer View by Ellen Meiksins Wood for a specific look at how the capitalism virus spread from England to the rest of the world, but she kind of disagrees with a lot of the historians above. A lot of the argument comes down to how you define capitalism and where it starts. Wood would argue that capitalism doesn’t “start” until the agrarian revolution in England, whereas historians like Arrighi and Braudel would place it a bit earlier in the merchant republics of Renaissance Italy and their financialised capital-intensive economies.

EDIT: Missed your last point, basically you need for there to be incentive to do labour saving technological advancement. Steam power already existed in Ancient Greece and Rome, it just wasn’t applied to labour saving things because there was no need. If you can accumulate power and capital via slaves and trade, labour is really cheap, and why would you bother?