OAuth2 and React
There are a few libraries out there that seem to deal with this.
Formidable Labs variant appears to be both active and supports some of the built in OAuth offerings on IOS and Android. So this might be the a good option:
As I'm using my own google domain I can set up OAuth as an internal mechanism with low effort - so this looks promising.
Update
After a review it appears Expo has this service built in, so we can enable this by calling:
expo install expo-google-app-authas per documentation here