🛠 Tooling: Use the create engine for network requests

[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

Splitting out of #1181: I'm onboarding this project to the new "create" engine in https://github.com/JoshuaKGoldberg/create. #1670 added usage of file creations. Another step will be having network requests such as GitHub branch protections and repo settings provided by blocks.

Additional Info

Linked issue in create: JoshuaKGoldberg/create#23

💖

[JoshuaKGoldberg]

For reference, here are the network requests sent in CTA today as part of >=1 mode runtime...

• octokit.rest.repos.get({ owner, repo }): in doesRepositoryExist, to check whether the repository exists
  • If it does, shell scripts around git remote add origin and git push -u origin main --force are sent
• octokit.rest.users.getAuthenticated(): in getGitHubUserAsAllContributor, to add the current user as an allcontributors contributor
• octokit.rest.repos.createUsingTemplate, octokit.rest.repos.createForAuthenticatedUser, or octokit.rest.repos.createInOrg: in createRepositoryWithApi
• octokit.rest.repos.update: in initializeRepositorySettings
• octokit.request('PUT /repos ... /branches/main/protection): in initializeBranchProtectionSettings
• octokit.request('GET .../labels'), octokit.request('POST .../labels'), octokit.request('DELETE .../labels'), and octokit.request('PATCH .../labels'): in initializeRepositoryLabels

Roughly. I might have missed some.

[JoshuaKGoldberg]

Will tackle first: #1768.