Make build_android publish to the staging repositories (#45468)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/45468

This should greatly reduce the time spent on build_npm_package
because we're moving all the publishing logic to build_android.

I need to do a bit more testing with nightlies to make sure that everything is published correctly.

Changelog:
[Internal] [Changed] - Make build_android publish to the stating repositories

Reviewed By: cipolleschi

Differential Revision: D59804015

fbshipit-source-id: be3f0b6e16f5fdbf760ec7a5e16c8e258e06dd28