docs(api): update and expand business documentation

Rewrite docs/api.md to provide a more structured overview of business
logic, core models, and authentication mechanisms. Include detailed
cURL examples for typical operations and add a new management
relationship diagram asset.

- Significant rewrite of docs/api.md with better formatting and content
- Add mermaid diagram for resource relationships
- Update README.md to reference the expanded documentation
- Add docs/管理关系图.png asset

README.md

@@ -21,6 +21,8 @@ EZ-API 是“控制平面”，负责管理事实来源 (Source of Truth)。
 
 ## API 端点
 
+> 补充文档（中文）：[`docs/api.md`](docs/api.md)
+
 ### 基础
 - `GET /health`
 - `GET /api/status/test`