[QA] Refactor code to create an admin API client

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The following discussion from !19785 (merged) should be addressed:

• @mlapierre started a discussion: (+2 comments)

  This method is almost identical to the one in qa/qa/runtime/feature.rb. What do you think about moving it to qa/qa/support/api.rb (from feature.rb as well) and renaming it something like admin_api_client (so that it doesn't conflict with api_client in qa/qa/resource/api_fabricator.rb or anywhere else it's included)?