Update pipeline setup for full e2e test run execution

What does this MR do and why?

Updates pipeline setup to correctly execute full e2e child pipeline after recent changes in gitlab-org/gitlab

MR acceptance checklist

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

• Commits include Changelog: trailer
• I have evaluated the MR acceptance checklist for this MR.