CE backport for gitlab-org/gitlab-ee!15433 (Expose DesignType#notes_count in GraphQL)

What does this MR do?

This is the CE backport of https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/15433.

Issue https://gitlab.com/gitlab-org/gitlab-ee/issues/13353.

• New after_commit callbacks have been added to Note to call #after_note_created and #after_note_destroyed on their noteable, so the noteable can perform tasks particular to them, like cache expiry.
• Refactors into a shared example some spec behaviour tests of a counter caching service

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry for user-facing changes, or community contribution. Check the link for other scenarios.
• [-] Documentation created/updated or follow-up review issue created
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content

Performance and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• [-] Tested in all supported browsers