I started programming in React Native, and I got used to use the syntax:
return await otherFunction();
React Native ships with Babel and some Babel presets, whereas React on the web is just React related code.
If you want to use async/await on the web today you'll need Babel and the correct transforms: https://babeljs.io/docs/plugins/transform-async-to-generator/
or the stage-1 presets, which is fairly common in React apps today. http://babeljs.io/docs/plugins/preset-stage-1/