Incorporate changelog checking?

A while back, we created the [`changelog-check` workflow in the `github-tools` repo] to ensure that changelogs were updated alongside changes in polyrepos and monorepos.

We should consider moving that logic to this tool. This way the workflow itself would be very simple (and we may not need to keep it in `github-tools`, it could be added directly to the module/monorepo templates).

Start by reading the changelog-check workflow in the github-tools repo and compare it with this tool's current entry points and module/monorepo templates. Define where the checking logic should live and how templates would invoke it; done means the existing changelog validation is incorporated without duplicating workflow logic.

Written by the indexing model from the issue text.