Remove repeat checkout step from diff-js-api-changes (fix CI) (#54865)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/54865

Removes introduced in D88654826, replaced with a `git fetch` with `--depth`.

This should fix CI runs on `main` (where we believe the extra checkout is clobbering the `yarn-install` step), and improve execution time.

Also shorten action name.

Changelog: [Internal]

Reviewed By: cipolleschi

Differential Revision: D89044330

fbshipit-source-id: 690eb5c7db9490e5f160e933d64eae6ac21464c8