Create a QA check for GitHub Actions that checks for breaking API changes

**Is your feature request related to a problem? Please describe.**
Sometimes, we unintentionally break API. It would be nice if we could detect this in a PR.

**Describe the solution you'd like**
A new matrix line in our QA / CI checks in GitHub Actions could be added to check our public API classes to see if they have had a breaking change (change of method signature or removal of method). We could also detect API additions. It would be okay for this check to fail, if the change is actually intended. But, having this check fail when such changes do occur in a PR will bring our attention to changes we might not have intended to make.

**Describe alternatives you've considered**
Catch it in code review manually (what we do now) or check periodically (what we tend to do at release time).

**Additional context**
N/A

Start by reading the existing QA/CI GitHub Actions matrix and inventorying the public Java API classes it should compare. Define how method-signature changes, removals, and additions are reported, including intentionally breaking changes. Done means a pull-request check flags these API changes in CI for review.

Written by the indexing model from the issue text.