Refactor Publish pipeline (take 2)

[Saadnajmi]

Please select one of the following

• I am removing an existing difference between facebook/react-native and microsoft/react-native-macos 👍
• I am cherry-picking a change from Facebook's react-native into microsoft/react-native-macos 👍
• I am making a fix / change for the macOS implementation of react-native
• I am making a change required for Microsoft usage of react-native

Summary

#1771 merged prematurely... so here's take 2.

This change refactors both our NPM Publish and NPM Publish Dry Run jobs to be much more correct, readable, and actually work. Namely, there's a few big changes:

1. Move the checking of what branch we're on to the top level vars.yml with nice names like isMain and isReleaseBranch so it's a lot easier to reason about
2. Create a new template apple-job-publish that contains most of the publish steps with a parameter for "build-type"

• This way, we can extract any references to the Branch name from these steps, and instead focus on the intent: what "type" of build/release are we publishing?

3. Use that template for both our PR check ("NPM Publish Dry Run") and our publish job

• With the variables we defined earlier (isMain and isReleaseBranch), it's now very easy to reason if we're doing a nightly or a release build.

All in all, very happy with this refactor :)

Changelog

[GENERAL] [FIXED] - Fix publish (attempt 2)

Test Plan

CI should pass