Fix diff-js-api-changes CI job (#54900)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/54900

Another attempt at fixing the failing `danger` job in GitHub Actions.

**Changes**

- Update `danger-pr` workflow to check out the Pull Request branch.
- Use `git fetch --deepen` in `diff-js-api-changes` job to fix computing PR merge base.

Changelog: [Internal]

Reviewed By: cipolleschi

Differential Revision: D89287799

fbshipit-source-id: 45708d3c051c60f8134c96b54cb2b13b93afa8dc