Cleanup after refactors to processing module

Follow-up PR to https://github.com/apache/druid/pull/17493 to address pending unaddressed comments.

This PR has:

[ ] been self-reviewed.
- [ ] using the concurrency checklist (Remove this item if the PR doesn't have any relation to concurrency.)
[ ] added documentation for new or modified features or behaviors.
[ ] a release note entry in the PR description.
[ ] added Javadocs for most classes and all non-trivial methods. Linked related entities via Javadoc links.
[ ] added or updated version, license, or notice information in licenses.yaml
[ ] added comments explaining the "why" and the intent of the code wherever would not be obvious for an unfamiliar reader.
[ ] added unit tests or modified existing tests to cover new code paths, ensuring the threshold for code coverage is met.
[ ] added integration tests.
[ ] been tested in a test Druid cluster.

apache / druid