docs: move model catalog out of shared

The model catalog is no longer a frontend/backend runtime contract.

Keeping it under shared made ownership misleading. It implied the catalog was
application code shared by runtime consumers, even though it now only supports
README links and public API documentation.

Move the catalog into public so it lives beside the docs surfaces that need it.
This gives the API docs a stable, served module and gives README readers a
linkable source without suggesting frontend or backend runtime dependency.

Render the API docs model list from the exported provider registry instead of a
hardcoded Claude/Cursor/Codex subset. That keeps Gemini and OpenCode visible and
makes future provider documentation changes flow through one docs-specific file.

Update README links, provider maintenance notes, and package files so published
artifacts include the standalone docs page and model catalog without relying on
the old shared path.

README.ko.md

@@ -60,7 +60,7 @@
 - **세션 관리** - 대화를 재개하고, 여러 세션을 관리하며 기록을 추적
 - **플러그인 시스템** - 커스텀 탭, 백엔드 서비스, 통합을 추가하여 CloudCLI 확장. [직접 빌드 →](https://github.com/cloudcli-ai/cloudcli-plugin-starter)
 - **TaskMaster AI 통합** *(선택사항)* - AI 중심의 작업 계획, PRD 파싱, 워크플로 자동화를 통한 고급 프로젝트 관리
-- **모델 호환성** - Claude, GPT, Gemini 모델 계열에서 작동 (`shared/modelConstants.js`에서 전체 지원 모델 확인)
+- **모델 호환성** - Claude, GPT, Gemini 모델 계열에서 작동 (`public/modelConstants.js`에서 전체 지원 모델 확인)
 
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