Replace the use of `airborne` with QA::Support::API which handles rate limits

A lot of tests currently use airborne directly and so, they do not handle rate limits gracefully. This issue is to shift to using QA::Support::API in those tests.

See this failure: https://ops.gitlab.net/gitlab-org/quality/staging/-/jobs/5586552

• gitlab-org/gitlab!163279 (merged)
• gitlab-org/gitlab!163425 (merged)
• gitlab-org/gitlab!163582 (merged)
• gitlab-org/gitlab!164311 (merged)
• gitlab-org/gitlab!165285 (merged)