Change snippet visibility to Private

What does this MR do?

Internal visibility was disabled in Production so the test always fails there. See https://docs.gitlab.com/ee/api/project_snippets.html. It makes more sense to create a Private snippet instead.

Closes #221016 (closed)

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• [-] Separation of EE specific content