Remove the 'flaky-examples-check' job as it's not reliable/used

Signed-off-by: Rémy Coutable <remy@rymai.me>

.gitlab/ci/rules.gitlab-ci.yml

@@ -493,13 +493,6 @@
       changes: *code-backstage-patterns
       when: on_success
 
-.test-metadata:rules:flaky-examples-check:
-  rules:
-    - <<: *if-merge-request
-      changes: *code-backstage-patterns
-      when: on_success
-
-
 ##############
 # YAML rules #
 ##############

.gitlab/ci/test-metadata.gitlab-ci.yml

@@ -37,22 +37,3 @@ update-tests-metadata:
     - retry gem install fog-aws mime-types activesupport rspec_profiling postgres-copy --no-document
     - source scripts/rspec_helpers.sh
     - update_tests_metadata
-
-flaky-examples-check:
-  extends:
-    - .default-tags
-    - .default-retry
-    - .test-metadata:rules:flaky-examples-check
-  image: ruby:2.6-alpine
-  stage: post-test
-  variables:
-    NEW_FLAKY_SPECS_REPORT: rspec_flaky/report-new.json
-  allow_failure: true
-  artifacts:
-    expire_in: 30d
-    paths:
-      - rspec_flaky/
-  script:
-    - '[[ -f $NEW_FLAKY_SPECS_REPORT ]] || echo "{}" > ${NEW_FLAKY_SPECS_REPORT}'
-    - scripts/merge-reports ${NEW_FLAKY_SPECS_REPORT} rspec_flaky/new_*_*.json
-    - scripts/flaky_examples/detect-new-flaky-examples $NEW_FLAKY_SPECS_REPORT

doc/development/testing_guide/flaky_tests.md

@@ -44,9 +44,8 @@ On our CI, we use [rspec-retry] to automatically retry a failing example a few
 times (see [`spec/spec_helper.rb`] for the precise retries count).
 
 We also use a home-made `RspecFlaky::Listener` listener which records flaky
-examples in a JSON report file on `master` (`retrieve-tests-metadata` and `update-tests-metadata` jobs), and warns when a new flaky example
-is detected in any other branch (`flaky-examples-check` job). In the future, the
-`flaky-examples-check` job will not be allowed to fail.
+examples in a JSON report file on `master` (`retrieve-tests-metadata` and
+`update-tests-metadata` jobs).
 
 This was originally implemented in: <https://gitlab.com/gitlab-org/gitlab-foss/-/merge_requests/13021>.