Use smaller health check suite to verify upgrades major/minor

What does this MR do and why?

Addresses the issue raised in: gitlab-org/quality/quality-engineering/team-tasks#2601 (closed)

It needs the counterpart MR gitlab!154264 (merged) to be merged first so there is a test suite to be run on update-major and update-minor scenarios

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.