Allow unauthenticated public snippet API calls

What does this MR do?

To be more consistent with how public visibility snippets can be accessed elsewhere, this MR is changing the REST API to allow public personal snippets to be accessed without user authentication.

Eventually the same will be applied to the Project Snippets REST API.

Refs #247530 (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

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.