One billion dollars is a lot to pay for a morning brew, but that’s what Abu Dhabi spent in September for a minority stake in Luckin Coffee, the Chinese chain with more than 36,000 global stores that built an empire on cheap drinks, relentless expansion and an app-first business model. But for the emirate, the deal is about more than coffee. Mubadala Investment Company, Abu Dhabi’s $385-billion sovereign wealth fund, has invested more than $20 billion in China in the last decade. Its stake in Luckin offers a glimpse into what the emirate sees in a Chinese economy that has…