react-native-watch-connectivity includes native code which is not included in the Expo Go app, so it cannot work with Expo Go. However according to the installation instructions it does not need anything special. Just autolinking. So it should work out of the box with a development build.
See also: Integrate the react-native-watch-connectivity library, directly with expo - #3 by wodin
If you want to generate the native projects you should use npx expo prebuild. This will use any config plugins you have specified in app.json to set things up as needed.
expo eject is no longer a thing.
However, as mentioned above, you should not need to prebuild to use react-native-watch-connectivity.