Remove usage of let_it_be to avoid spec-ordering failures

What does this MR do and why?

This MR removes some usage of let_it_be that was creating order-dependent failures in some of the specs in this file. Because varying permissions that get assigned in each spec, we should dispose of the setups and recreate them every time.

How to set up and validate locally

h/t @kwiebers: !95756 (comment 1091439663)

1. On master: bundle exec rspec './spec/services/ci/create_downstream_pipeline_service_spec.rb[1:4:15:1,1:4:17:1,1:4:18:1,1:4:19:1:1,1:4:20:1:1]'
2. Again on this feature branch fix-flaky-downstream-pipeline-service-spec

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.