Move the 'dont-interrupt-me' job to the 'sync' stage

What does this MR do?

This should avoid scheduled pipelines to be canceled while cache-repo is running and before dont-interrupt-me has started.

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Separation of EE specific content

Closes #212845 (closed).