🚀 Feature: Use all-contributors (or an equivalent) without creating a root-level file (.all-contributorsrc)

### Bug Report Checklist

- [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

Recreating #1845 more generally: I want fewer root-level config files in this template. Tooling fatigue is a real problem for web developers. Every file added to repositories contributes to that fatigue.

IMO the `.all-contributorsrc` file is theoretically unnecessary. The main information it stores is duplicated in a README.md section. I'd like to get rid of the file and just have contributors inferred from the README.

I'd requested this in https://github.com/all-contributors/all-contributors/issues/808. No response yet. The all-contributors project hasn't had very consistent maintenance for a few years now so I'm not optimistic it will be addressed soon. (it's a great project, just I don't think there are enough people working on it to meet the issue-triaging demand)

One of two things is going to happen this year:

* The all-contributors project makes the `.all-contributorsrc` optional
* I'll create my own version of the project that runs purely on GitHub Actions

### Additional Info

That list is in order of preference. I really don't want to create a second, seemingly-almost-the-same option folks would have to choose from. And I certainly don't want to have to take on more maintenance work with it (I've got a lot of other, higher impact things to do!). But the goal of reducing root config file count by 1 is worth it.

I'll keep this as `status: blocked` for a while, to give the all-contributors folks a chance to catch up on issues. I would feel bad making an alternative after only, say, a couple of months of the issue pending triage.

💖