🚀 Feature: Use pnpm as a Node.js environment manager

### Bug 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/create-typescript-app/issues?q=is%3Aissue) and found none that matched my issue.

### Overview

Since the project uses `pnpn` for installing packages, why not streamline it for Node.js environment installs? This will allow you to built-in a check whether the current environment on the machine matches the recommended version. Along with removing the `.nvmrc` file.

1. Check if recommended version exists:
```
$ pnpm env list

16.20.2
20.6.0
```
2. Install and use if not found:
```
$ pnpm env use 18.17.1

Fetching Node.js 18.17.1 ...
Node.js 18.17.1 is activated
```
3. Profit 💵

### Additional Info

Official docs: https://pnpm.io/cli/env