Port fixes to release scripts to use GITHUB_REF and GITHUB_REF_NAME variables (#45066)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/45066

This changes ports in main the fixes we had to make to the release scripts to run properly in release mode.

This includes the commits:

* https://github.com/facebook/react-native/commit/375c88478c985976e1b59dfa7353042a18b4d132
* https://github.com/facebook/react-native/commit/609c7c05b13214f2a834b251de095243f8dcbf68
* https://github.com/facebook/react-native/pull/45062

## Changelog:
[Internal] - Fix release scripts to run properly in release mode

Reviewed By: cortinico

Differential Revision: D58782925

fbshipit-source-id: b096909d5f8281809ee3c2a01eefda1d19f32936