Push_over_http_spec E2E test failed during 12.4.x to 12.5.x Geo HA upgrade

https://gitlab.com/gitlab-org/quality/looping-pipeline/-/jobs/420804130

Investigate why, while upgrading a Geo HA setup from 12.4.8 to 12.5.7, the qa/specs/features/browser_ui/3_create/repository/push_over_http_spec.rb failed after running successfully for ~14 minutes. Failure was first noticed during update of the primary deploy node.

Failures:
   1) Create Git push over HTTP user pushes code to the repository
      Failure/Error:
        project_push = Resource::Repository::ProjectPush.fabricate! do |push|
          push.file_name = 'README.md'
          push.file_content = '# This is a test project'
          push.commit_message = 'Add README.md'
        end
      
      QA::Resource::ApiFabricator::ResourceFabricationFailedError:
        Fabrication of QA::Resource::Group using the API failed (400) with `{"message":"Failed to save group {:path=\u003e[\"has already been taken\"]}"}`.