[Docs] Add Anthropic-compatible API documentation (#28522)

Co-authored-by: zijiexia <37504505+zijiexia@users.noreply.github.com>
Co-authored-by: Zijie Xia <zijie.xia@radixark.ai>
Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>

docs_new/docs/basic_usage/overview.mdx

@@ -4,6 +4,7 @@ description: Core APIs and common usage patterns for SGLang.
 ---
 
 - [OpenAI-Compatible APIs](./openai_api_completions) — Chat completions, vision, and embeddings
+- [Anthropic-Compatible API](./anthropic_api) — `/v1/messages`, including Claude Code integration
 - [Ollama API](./ollama_api)
 - [Offline Engine API](./offline_engine_api)
 - [Native API](./native_api)