chore: auth example doc

[valentinbeggi]

Greptile Summary

Adds the Auth example app to the documentation showcase. A new card is added to the main showcase index page (docs/showcase.mdx) linking to the auth detail page, and a hero image is added to the auth detail page (docs/showcase/auth.mdx).

• New "Auth" card added to the showcase index, following the existing card pattern (GitHub link only, no live demo link).
• Hero image added to docs/showcase/auth.mdx, though placed before the introductory text rather than after it as in other showcase pages.

Confidence Score: 5/5

• This PR is safe to merge — it only adds documentation content with no code changes.
• The PR consists entirely of documentation changes (MDX files) that add a showcase card and hero image. There are no logic, syntax, or security concerns. The only note is a minor style inconsistency in image placement order.
• No files require special attention.

_{Last reviewed commit: 16a51fd}

[greptile-apps]

_{2 files reviewed, 1 comment}

_{Edit Code Review Agent Settings | Greptile}

[greptile-apps]

Inconsistent image placement order

In other showcase pages (e.g., capitals.mdx, ecommerce-carousel.mdx), the hero image is placed after the introductory text paragraph. Here the image is placed before the text. Consider swapping the order to match the existing pattern:

Suggested change

	<img
	src="/images/showcase-auth.png"
	alt="Auth"
	style={{ width: "100%", maxWidth: "960px", borderRadius: "12px" }}
	/>
	Auth is an example that demonstrates full OAuth authentication using WorkOS AuthKit, with a personalized coffee shop finder widget that displays user-specific favorites.
	<img
	src="/images/showcase-auth.png"
	alt="Auth"
	style={{ width: "100%", maxWidth: "960px", borderRadius: "12px" }}
	/>

_{Note: If this suggestion doesn't match your team's coding style, reply to this and let me know. I'll remember it for next time!}

Prompt To Fix With AI

This is a comment left during a code review.
Path: docs/showcase/auth.mdx
Line: 6:10

Comment:
**Inconsistent image placement order**

In other showcase pages (e.g., `capitals.mdx`, `ecommerce-carousel.mdx`), the hero image is placed *after* the introductory text paragraph. Here the image is placed *before* the text. Consider swapping the order to match the existing pattern:

```suggestion
Auth is an example that demonstrates full OAuth authentication using WorkOS AuthKit, with a personalized coffee shop finder widget that displays user-specific favorites.

<img
  src="/images/showcase-auth.png"
  alt="Auth"
  style={{ width: "100%", maxWidth: "960px", borderRadius: "12px" }}
/>
```

<sub>Note: If this suggestion doesn't match your team's coding style, reply to this and let me know. I'll remember it for next time!</sub>

How can I resolve this? If you propose a fix, please make it concise.