🧪 Testing: Consider adding end-to-end tests

### Tooling Report Checklist

- [x] I have tried restarting my IDE and the issue persists.
- [x] I have pulled the latest `main` branch of the repository.
- [x] I have [searched for related issues](https://github.com/JoshuaKGoldberg/formatly/issues?q=is%3Aissue) and found none that matched my issue.

### Overview

Continuing discussion from https://github.com/JoshuaKGoldberg/formatly/pull/131#discussion_r2059544727: prior to #131, this repo's only had unit tests. But then sometimes end-to-end/integration-level behavior has been broken (e.g. #125/#126 -> #127). Would it make sense for this repo to include some kind of end-to-end testing?

### Additional Info

Maybe, one end-to-end test for each of the supported formatters? Where each end-to-end test runs `formatly` on the CLI in a directory that's set up with the formatter?

🧼