🚀 Feature: Drop end-user dependency on gh

[JoshuaKGoldberg]

Bug Report Checklist

• I have tried restarting my IDE and the issue persists.
• I have pulled the latest main branch of the repository.
• I have searched for related issues and found none that matched my issue.

Overview

The GitHub CLI (gh) is really convenient. I use it a lot personally. Right now, gh is used for two things in the repo's hydration/setup scrips:

1. Getting a GitHub auth token for the user: search gh auth in the code
2. Running commands to modify the repository: search gh (note the trailing space)

However, not everyone using this template might be a gh user already. It's inconvenient that you'd have to use it. Let's remove the dependency on having that tool installed. I think that'll mean two changes:

1. For the auth token: try running the same gh auth scripts as before, and if they fail, fall back to a CLI flag like --github-auth
2. Switch to using Octokit instead of gh ... for any API calls

Additional Info

No response

[github-actions]

🎉 This is included in version v1.71.0 🎉

The release is available on:

• GitHub releases
• npm package (@latest dist-tag)

Cheers! 📦🚀