Resolves #37695 - Use clsx instead of classnames (#37708)

* Add rule to disallow `classnames`

* Initial pass

* `classnames/dedupe` → `@wordpress/token-list`

* Add changelog

* Use valid changelog types

* Remove file from eslint exclusions

* Change post-rebase use of classnames

* More changelog format compliance fixes

* Bump versions

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/9451810503

Upstream-Ref: Automattic/jetpack@40a8492