publish template on publishing release (#45327)

Summary:
Call the react-native-community/template GHA to trigger a new release when we publish a react-native release. This then waits to confirm that the package is published.

See react-native-community/template#36 for the matching change

Changelog: [General][Added] trigger template publish

Pull Request resolved: https://github.com/facebook/react-native/pull/45327

Test Plan: Not sure on the best way forward here.

Reviewed By: cipolleschi

Differential Revision: D59467829

Pulled By: blakef

fbshipit-source-id: 091269e7ecdae5801ac7c03a1ede54452ae99b24