🚀 Feature: Add a mode for repository initialization

[JoshuaKGoldberg]

Bug Report Checklist

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

Overview

Right now, producer and runner APIs don't understand the idea of a "mode": whether a repository is being newly created, initialized from a template, or migrated/updated from older/other templating. But each of those three modes has added logic to run.

This issue tracks the creation mode: creating a new repository and linking it to one on GitHub.

Additional Info

Tracking issue in CTA: JoshuaKGoldberg/create-typescript-app#1764

create-typescript-app does this by deleting the dependencies and files from its own source that are unnecessary - thus leaving files behind. I think from the template's perspective it'd be cleaner to just delete everything in the repository and then re-run creation.

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