Merge branch 'andrey-readiness-check-cleanup' into 'master'

Improve gitlab readiness check in e2e tests

See merge request https://gitlab.com/gitlab-org/gitlab/-/merge_requests/167766



Merged-by: Tiffany Rea <trea@gitlab.com>
Approved-by: Tiffany Rea <trea@gitlab.com>
Co-authored-by: Andrejs Cunskis <acunskis@gitlab.com>