feat: remove codecov token from README.md (#636)

## PR Checklist

- [x] Addresses an existing open issue: fixes #453
- [x] That issue was marked as [`status: accepting
prs`](https://github.com/JoshuaKGoldberg/template-typescript-node-package/issues?q=is%3Aopen+is%3Aissue+label%3A%22status%3A+accepting+prs%22)
- [x] Steps in
[CONTRIBUTING.md](https://github.com/JoshuaKGoldberg/template-typescript-node-package/blob/main/.github/CONTRIBUTING.md)
were taken

## Overview

I'm pretty sure the token is just for private repos. I don't mind
removing it for now. If someone has a private repo they can always add
it back in.

Author: JoshuaKGoldberg

README.md

@@ -11,7 +11,7 @@
 <!-- prettier-ignore-end -->
 	</a>
 	<a href="https://codecov.io/gh/JoshuaKGoldberg/template-typescript-node-package" target="_blank">
-		<img alt="Codecov Test Coverage" src="https://codecov.io/gh/JoshuaKGoldberg/template-typescript-node-package/branch/main/graph/badge.svg?token=eVIFY4MhfQ"/>
+		<img alt="Codecov Test Coverage" src="https://codecov.io/gh/JoshuaKGoldberg/template-typescript-node-package/branch/main/graph/badge.svg"/>
 	</a>
 	<a href="https://github.com/JoshuaKGoldberg/template-typescript-node-package/blob/main/.github/CODE_OF_CONDUCT.md" target="_blank">
 		<img alt="Code of Conduct: Enforced 🤝" src="https://img.shields.io/badge/code_of_conduct-enforced_🤝-21bb42" />

src/hydrate/steps/writeReadme.ts

@@ -71,7 +71,7 @@ function generateTopContent(values: HydrationInputValues) {
 	}" target="_blank">${
 		values.unitTests
 			? `
-	<img alt="Codecov Test Coverage" src="https://codecov.io/gh/${values.owner}/${values.repository}/branch/main/graph/badge.svg?token=INSERT_CODECOV_TOKEN_HERE"/>`
+	<img alt="Codecov Test Coverage" src="https://codecov.io/gh/${values.owner}/${values.repository}/branch/main/graph/badge.svg"/>`
 			: ""
 	}
 	</a>