Feature: Create new branch for open PRs

Hi there!

Right now when Claude is triggered on an open PR (via `@claude` mentions), it pushes commits directly to the PR branch. I've noticed this can be limiting in some workflows:

1. CI checks don't seem to run because commits from `github-actions[bot]` don't trigger workflows
2. Changes go directly into the PR without a way to review them separately first

I saw this mentioned in #319 and #828.

Would it make sense to have an option to create a new branch from the PR branch instead of pushing directly? Something like:

```yaml
- uses: anthropics/claude-code-action@v1
with:
use_new_branch_for_open_prs: true
```

If enabled, it could:
- Create a new branch from the PR's head branch (like `claude/pr-123-fix`)
- Commit changes there
- Provide a link to create a PR from that branch back to the original PR branch

This might let CI run on the new branch, and give a chance to review the changes before merging.

**Example workflow:**
1. I have PR `#123` from `feature-branch`
2. I comment `@claude fix the failing tests`
3. Claude creates `claude/pr-123-fix` from `feature-branch`
4. CI could run on the new branch
5. I could review and merge it back to `feature-branch`

This would be opt-in (default `false`) to avoid changing existing behavior. If this seems useful, I'd be happy to try implementing it!