Remove process.exit calls from publish-npm and throw errors instead (facebook#43039)

Summary:
Pull Request resolved: facebook#43039

Changelog: [Internal] - `publish-npm.js` is a [script we call in our CI](https://www.internalfb.com/code/fbsource/[c0b8566ac0d66c2c0282eeb597bfb54bedf757c6]/xplat/js/react-native-github/.circleci/configurations/jobs.yml?lines=1243) to publish the react-native package and others.

Currently, the script leverages `exit/process.exit` to terminate early in a couple of places which makes the code hard to test because our tests don't truly early exit when `exit/process.exit` is called.

This change removes any explicit `exit` calls and instead leverages the uncaught error to terminate the process and set the non-zero exit code. This makes our tests more accurate to the real control flow of the script.

I've also updated the tests to better capture what we're actually testing by mocking at a higher level.

Reviewed By: cipolleschi

Differential Revision: D53792754

fbshipit-source-id: 9293bb9a95430c50052db36c0e6f6c1ba348107f

Author: lunaleaps