Update design discussions to use GitLab UI components

What does this MR do?

Updates app/assets/javascripts/design_management/components/design_notes components to use GitLab UI components and utility classes. Also, this MR fixes emitted events names to be kebab-cased

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides

Availability 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
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Issue: #219730 (closed)