Does the sage's "One for the World" reflect China's traditional analogical thinking?

No, it reflects China's traditional holistic thinking.

China's traditional holistic thinking is intuitive thinking based on experience. Holistic thinking, the so-called holistic thinking, means that heaven and earth, man and society are closely linked as a whole, and heaven and earth, man, man and heart are in a whole system, and the elements of each system are interdependent. Mencius said, "A gentleman takes orders, but keeps one spirit and rises and falls with heaven and earth." Zhuangzi said: "Heaven and earth coexist with me, and everything is one with me." The Yi copula says, "Everything in the world is true." Laozi said: "saints hold a world view." Xunzi said, "One hundred Wang Zhidao is enough.