doc: renamed swagger to openapi

[mjjabarullah]

Summary by CodeRabbit

• Documentation
  • Updated Better Auth integration guide to use OpenAPI terminology instead of Swagger.
  • Revised code snippets to import and configure the @elysiajs/openapi plugin.
  • Clarified that schema generation remains unchanged; no runtime modifications required.
  • Improved consistency with current tooling and ecosystem standards.
  • Ensures developers can follow the updated examples without migration steps or breaking changes.

[coderabbitai]

Walkthrough

Updates documentation to replace references and code samples from @elysiajs/swagger to @elysiajs/openapi in better-auth integration docs. No API surface or functional logic changes beyond plugin naming in examples.

Changes

Cohort / File(s)	Summary
Docs: OpenAPI plugin rename docs/integrations/better-auth.md	Replaced “swagger” with “openapi”; updated import/use from @elysiajs/swagger to @elysiajs/openapi; preserved OpenAPI schema generation flow; no public/API changes.

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~3 minutes

Poem

I twitch my ears at docs so neat,
From swagger’s waltz to openapi’s beat.
A hop, a swap, the samples shine,
Same schema trail, a different sign.
Thump-thump! I stamp in tidy glee—
Carrots for clarity, docs set free. 🥕

Pre-merge checks and finishing touches

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title Check	✅ Passed	The title clearly and concisely summarizes the primary change of renaming references from Swagger to OpenAPI in the documentation, matching the updates made in the code samples and text without extraneous detail.
Docstring Coverage	✅ Passed	No functions found in the changes. Docstring coverage check skipped.

✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment

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📜 Recent review details

Configuration used: CodeRabbit UI

Review profile: CHILL

Plan: Pro

📥 Commits

Reviewing files that changed from the base of the PR and between 99e9af8 and bfcc809.

📒 Files selected for processing (1)

• docs/integrations/better-auth.md (1 hunks)

🔇 Additional comments (1)

docs/integrations/better-auth.md (1)

129-145: OpenAPI plugin rename looks good.

The updated import and usage now align with @elysiajs/openapi; the sample remains coherent after the rename.

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