Action requires GITHUB_TOKEN even for public repositories

If the action is configured not to push and the configured repository is public, then the `GITHUB_TOKEN` should not be required, since the action should be able to clone the repository without it.

Currently the action fails due to the following validation, not because the action can't actually clone the repo.

```js
if (ghRepository) {
validateGitHubToken('gh-repository', githubToken, 'to clone the repository');
}
```

This is undesirable because it unnecessarily leads users to create PATs or fine-grained tokens, increasing their security exposure.

Start at the shown `ghRepository` validation and trace how repository cloning and push configuration are handled. The change is done when a public repository configured not to push can be cloned without `GITHUB_TOKEN`, while configurations that still require authentication continue to validate it.

索引モデルが issue の本文から書いたものです。