🚀 Feature: Support for reusable template application, i.e. "components"

[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

Many other template projects support a use case of reusable chores within a repository. A couple of quick examples:

• In backend code, creating a new server handler like src/handlers/${name}.ts + a test in src/handlers/{name}.test.ts + a line in src/handlers.ts like addHandler({name});.
• In frontend code, creating a new component in src/components/{name}.tsx + a test in src/components/{name}.test.tsx. Maybe also a line in src/components/index.ts of export * from './src/components/{name}.js';.

This is a deceptively hard problem to solve well. If it was just creating files like src/components/{name}.tsx then it would be somewhat as straightforward as reusing the existing Creation ideas from the rest of the engine. But also touching files like src/components/index.ts makes it much more tricky... 🤔

Additional Info

I'm not going to put effort into this for a while. milestone/2 Blocks Launch will happen first. Heck, I might not even tackle this until after milestone/3 Broad Launch Marking as blocked for now.

💖