🐛 Bug: Releases can become broken after two quick pushes to main again

### 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.

### Expected

Pushing two "meaningful" commits -as in, ones that should cause a new package publish- to `main` should not cause failures. Both should be released in 1-2 packages on npm.

### Actual

The saga of #556 -> #862 continues: if two meaningful commits are pushed to `main` quickly, the release flow of the first one will fail to `git push` because the second is running.

See the build failures from, in order:

1. https://github.com/JoshuaKGoldberg/create-typescript-app/commit/fda4ec9d9624945476326d552af8462d6eb5b392
2. https://github.com/JoshuaKGoldberg/create-typescript-app/commit/b39ae009b36c80dfdc3f50745a404dba0e0b77b4

### Additional Info

I don't yet know how to solve this... but accepting PRs if someone does.

🎁