IMO updating the repository settings would be simpler: https://docs.github.com/en/repositories/configuring-branches-and-merges-in-your-repository/configuring-pull-request-merges/managing-the-automatic-deletion-of-branches

I also came across this page, but it seems like a better option is to use workflow so as not to delete all the branches (but only delete the "update" branches)

Deleting all branches seems like a questionable decision