Migrate to Publish to BCR actions workflow

The GitHub app for publishing modules to the BCR is now deprecated. Please consider upgrading to the new GitHub Actions workflow so that future publishes will continue to work.

See the documentation at https://github.com/bazel-contrib/publish-to-bcr.

Let me know if you need any assistance with the migration.

Start by inspecting the repository's GitHub Actions configuration and the publish-to-bcr documentation linked in the issue. Replace the deprecated publishing integration with the documented workflow, then verify that the configuration supports future module publishes without relying on the GitHub app.

Written by the indexing model from the issue text.