🚀 Feature: Hydration script should call the same GitHub APIs as the setup script

[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

This repo has two scripts that can run to set up a repository:

• "Hydration" (added in feat: add hydration script for existing repos #441): initializes an existing repository
• "Setup": sets up a newly cloned repository from the template

Right now, the setup script calls to GitHub APIs to set up repository labels and assorted other GitHub repository settings. But the hydration script doesn't do that...

...yet! Let's have the hydration script call to those same APIs.

Additional Info

I think we should find a way to share code between the two scripts. It'd be annoying to have the code exist in two locations. Perhaps moving the setup script to inside src/? Note that the setup script should be written in .js files so that folks don't have to run pnpm build before running it. We'd want to enable checkJs in tsconfig.json, I think. #468

We'll also want at least one --skip-* flag the same way that the setup script does. I'd want to be able to run this thing without modifying the main/upstream repository!

[JoshuaKGoldberg]

Ah, this was resolved by #489.