Hi! I discovered how to run react-native inside of the macOS menu bar, here is a link to a running template project:
https://github.com/ospfranco/rn-macos-menubar-template
And here are the steps if you want to do it yourself:
https://ospfranco.github.io/post/2020/05/23/how-to-make-a-react-native-menu-bar-app-for-mac-os/