I have my apps running and the App.js file contains ONESIGNALAPPID = 'my id' so does the OneSignal App ID field in /studio/settings.

Yes, it's the same ID like in studio > settings

I have configured both the iOS and Android in my onesignal account. Do I understand correctly that I now have to go through all the steps described here https://documentation.onesignal.com/docs/react-native-sdk-setup to install sdk and then recompile my apps?

No, you don't need to do it, however after setting/changing ONESIGNALAPPID you need to recompile the app.,