Make the workflow file responsible that commits changes to built files more maintainable

[desrosj]

The commit-built-file-changes.yml file currently contains all of the logic that commits and pushes any missed changes to built files. This does not work when it comes to non-default branches because updates to the logic would need to be backported, which is unsustainable.

[61286] introduced a new Grunt task that will remove this file when grunt post-branching is run in a newly created branch. This is not ideal as it reintroduces the possibility of committing something that's missing changes to built files.

If this file can be updated to take advantage of the reusable workflow pattern, it can remain in old branches and call a reusable file in trunk, eliminating the maintenance burden.

After this is solved in trunk, the workflow would need to be reintroduced into the 6.8 & 6.9 branches to accompany the check-built-files.yml workflow.

Additional context: ​https://github.com/WordPress/wordpress-develop/pull/10512#discussion_r2525836190

Props @peterwilsoncc, @johnbillion for participating in that discussion.