Resolve "Refactor design_discussion.vue to use ApolloMutation component"

What does this MR do?

Refactors Apollo mutations to use ApolloMutation component in place of $apollo.mutate, in addition to some minor cleanup. Relevent Jest test has been updated to support this change.

Does this MR meet the acceptance criteria?

Conformity

• [ ] Changelog entry
• [ ] 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

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

Related issue: #35070 (closed)