RN: Move `tools/api` to `private/cxx-public-api` (#51859)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/51859

Moves `tools/apis` to `private/cxx-public-api` and cleans up a few things:

- Clean up the `BUCK` file a bit.
- Deduplicate relative paths in scripts.
- Prefix the private package name with `react-native/`.

Changelog:
[Internal]

Reviewed By: huntie

Differential Revision: D76091765

fbshipit-source-id: 6fac7423f9d205085b0b21465f65075a850b61e2