Refactor draft_note_spec.js to Vue test utils (CE backport)

What does this MR do?

CE backport of https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/9486.

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated via this MR
• Documentation reviewed by technical writer or follow-up review issue created
• Tests added for this feature/bug
• Tested in all supported browsers
• Conforms to the code review guidelines
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to the database guides
• Link to e2e tests MR added if this MR has Requires e2e tests label. See the Test Planning Process.
• Security reports checked/validated by reviewer