Remove getChildInstances in project_header_spec and project_search_spec

What does this MR do?

This removes some of the uses of getChildInstances. This was causing issues with https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/9001

• It rewrites project_header_spec in vue-test-utils
• It rewrites a spec in project_search_spec

What are the relevant issue numbers?

Part of #9594 (closed)

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.
• EE specific content should be in the top level /ee folder
• For a paid feature, have we considered GitLab.com plans, how it works for groups, and is there a design for promoting it to users who aren't on the correct plan?
• Security reports checked/validated by reviewer