Allow unauthenticated public project snippet API access

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 project snippets to be accessed without user authentication, inline with the similar PersonalSnippet changes implemented here !44135 (merged)

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.