Document new "auth" playground display type

[mintlify]

Added documentation for the new playground: "auth" display type that dynamically shows the interactive API playground based on user authentication and group membership. This feature allows restricting interactive API testing to specific user groups while still allowing page visibility.

Files changed

• api-playground/overview.mdx - Added "auth" to display type options and included new section with examples
• api-playground/mdx-setup.mdx - Added "auth" to playground options list with detailed usage examples

Generated from feat: add "auth" display type for playground @lawreka

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Note

Low Risk
Documentation-only changes that don’t affect runtime behavior; primary risk is minor user confusion if wording/metadata examples are incorrect.

Overview
Documents a new playground: "auth" / playground: 'auth' display mode for the API playground in both the docs.json configuration (api.playground.display) and per-page frontmatter.

Adds an authentication + groups-based visibility section with an example using public: true and groups, and clarifies the resulting behavior (interactive for matching authenticated users, hidden otherwise).

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