Fix treeSaver and treeRestorer specs

This MR removes remains of use_legacy_pipeline_triggers feature flag that was removed 3 months ago: !21732 (merged), but due to some refactoring, it's still present in the code, and it was causing some issues when calling:

 allow(Feature).to receive(:enabled?) { true }

!29141 (comment 320203377)

It will also remove some redundant code, that was unintentionally left in !29141 (merged)

I also included a temporary fix for failing pipelines on master from !29235 (closed)

Conformity

• Changelog entry (https://docs.gitlab.com/ee/development/documentation/workflow.html#when-documentation-is-required))
• Code review guidelines
• Merge request performance guidelines

Closes #214003 (closed)