Extract `changelog-check` to separate action

The `changelog-check` workflow helps us ensure that changelogs are updated alongside changes in polyrepos and monorepos.

Currently, when we make use of this workflow in other repos we need to pin to a specific commit ID. This is cumbersome because it means that if we want to make a change to the workflow we now need to go through each repo by hand and update the commit ID.

If we extracted this workflow to an action, we could start using version strings such as `v1`. As long as new changes were backward compatible they would automatically get propagated to all of the repos.

Start by locating the existing changelog-check workflow and reviewing how other repositories consume it. Extract it into a versioned GitHub Action, update the usage model to support v1-style references, and verify that changelog checks still work for both polyrepos and monorepos.

Written by the indexing model from the issue text.