Backport of 'Simplify db:check-schema CI job'

What does this MR do and why?

Backport CI/CD job optimization done in master: Simplify db:check-schema CI job (!197855 - merged)

Contributes to Backport "Simplify db:check-schema CI job" (#558291 - closed)

MR acceptance checklist

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

• This MR is backporting a bug fix, documentation update, or spec fix, previously merged in the default branch.
• The MR that fixed the bug on the default branch has been deployed to GitLab.com (not applicable for documentation or spec changes).
• The MR title is descriptive (e.g. "Backport of 'title of default branch MR'"). This is important, since the title will be copied to the patch blog post.
• Required labels have been applied to this merge request
  • severity label and bug subtype labels (if applicable)
  • If this MR fixes a bug that affects customers, the customer label has been applied.
• Set the milestone of the merge request to match the target backport branch version.
• This MR has been approved by a maintainer (only one approval is required).
• Ensure the e2e:test-on-omnibus-ee job has either succeeded or been approved by a Software Engineer in Test.

Note to the merge request author and maintainer

If you have questions about the patch release process, please:

• Refer to the patch release runbook for engineers and maintainers for guidance.
• Ask questions on the #releases Slack channel (internal only).
• Once the backport has been merged, the commit changes will be automatically deployed to a release environment that can be used for manual validation. See after merging runbook for details.