https://lp.jetbrains.com/qodana/
Watch the video, the last sections show how integrate Qodana with GHA.
Not sure if it's free of use, but might be a good complement/alternative to CodeClimate.
CodeClimate only watches a single branch (in free plan), while Codana might watch all branches.
This is a suggestion, not sure if we want to do it, requires more analysis.