Three months ago, Sonya, a 25-year-old who works at a major mobile gaming company and moonlights as a tutor, made one of the toughest decisions of her life: She left Russia. She had an old but cozy communal apartment with her boyfriend and two other roommates in Moscow’s city center, a tight-knit group of friends, and spent several days a week taking classes at a local dance academy—her lifelong passion. “It’s my home. My family, friends are there. My whole life. How can you possibly abandon all these things?" she told Fortune. But like countless other young educated Russians, Sonya,...