🚀 Feature: Switch from lint-staged to nano-staged

### Feature Request Checklist

- [x] I have looked at the latest version of the project.
- [x] I have [searched for related issues](https://github.com/JoshuaKGoldberg/create-typescript-app/issues?q=is%3Aissue) and found none that matched my issue.

### Overview

[`lint-staged` is 1.91 MB](https://packagephobia.com/result?p=lint-staged). [`nano-staged` is 58.9 kB](https://packagephobia.com/result?p=nano-staged). It'd be nice to use the smaller package for a devDependency.

### Additional Info

@cylewaitforit and I were talking about how this could be a precursor to #2363.

I've noticed that `nano-staged` isn't always under maintenance. For example, https://github.com/usmanyunusov/nano-staged/pull/52 has been open for several months without response. However, `lint-staged` _also_ has many issues open without response, so 🤷 no perfect options here.

🎁