Test: fix order dependent readiness_check spec

What does this MR do and why?

Test is flaky and can break master (e.g. https://gitlab.com/gitlab-org/gitlab/-/jobs/8107722590)

Resolves gitlab-org/quality/engineering-productivity/master-broken-incidents#9005 (closed)

To reproduce: bundle exec rspec -O .rspec_internal ./spec/tools/readiness_check_spec.rb

Test is passing in this job: https://gitlab.com/gitlab-org/gitlab/-/jobs/8107842001