Investigate `parallel_push_checks` feature flag
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### Problem
Feature flag `parallel_push_checks` was introduced to improve the performance of push checks in https://gitlab.com/gitlab-org/gitlab/-/merge_requests/45668+.
It's currently enabled only for https://gitlab.com/gitlab-com/www-gitlab-com.
### Proposal
Review the code and discussion in https://gitlab.com/gitlab-org/gitlab/-/merge_requests/45668 to decide if this change should be enabled for all projects.
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