🚀 Feature: create private repos

### Bug Report Checklist

- [X] I have pulled the latest `main` branch of the repository.
- [X] I have [searched for related issues](https://github.com/JoshuaKGoldberg/create-typescript-app/issues?q=is%3Aissue) and found none that matched my issue.

### Overview

I'm experimenting with creating a new project. For now I want it to be private, I'll probably make it public later when I'm happy with what i've got. At present, the only type of repos you can create are public. Would it be good to be able to create private repos as well?

### Additional Info

One thing to bear in mind, is that some of the bundled tooling (Renovate etc) will only work on public repos for free I think. That may be an issue - or maybe something that can enabled later?

No files, tests, or entry points are identified in the issue. Start by locating the repository-creation flow and checking how visibility is selected; then determine how private repositories affect bundled tooling such as Renovate and define the supported behavior before implementation.

Written by the indexing model from the issue text.