Improve published packages: `arethetypeswrong/cli`

Consider introducing [arethetypeswrong/cli](https://github.com/arethetypeswrong/arethetypeswrong.github.io/tree/main/packages/cli) as a CI check.

We will definitely also have things to fix before this would be viable in CI. 😉

Start by reviewing the linked arethetypeswrong/cli package and the repository's existing CI and package-publishing setup. Identify the fixes required before the tool can run reliably in CI; done means those blockers are resolved and the check is integrated, but the issue does not define the specific fixes or files.

Written by the indexing model from the issue text.