[QA] Use public_email instead of email since it's available

What does this MR do?

This makes sure we fetch public_email from the response API instead of email which is only available to admins.

This also add tests for the User resource.

What are the relevant issue numbers?

Closes gitlab-org/quality/staging#27 (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.
• Security reports checked/validated by reviewer