docs: GET /api/test/is-initialized public endpoint missing from behaviors.md

[evan-zhang11]

Documentation Gap

Endpoint: GET /api/test/is-initialized
Auth: Not required (public)
Handler: handlers.rs → check_is_initialized()

Current Behavior

Returns whether the system has been initialized (i.e., whether the initial admin user has been created):

// Response 200
{ "initialized": true }

On internal error:

// Response 500
{ "error": "Failed to check initialization status: ..." }

Impact

• Low (P2): This is a utility endpoint used by the frontend login/init flow
• It's publicly accessible without authentication, which is a deliberate design choice (the frontend needs to know whether to show the init or login page)
• Not documenting it could lead to confusion about the bootstrapping flow

Suggested Fix

Add a new behavior contract entry:

ID	Module	Behavior	Verification	Layer	Priority
AUTH-005	初始化检查	GET /api/test/is-initialized 无需认证，返回系统是否已初始化。前端用于决定显示 /init 还是 /login 页面	200 + {initialized: boolean} / 500	Integration	P2

Context

• Discovered during daily documentation review (2026-07-31)
• Related to AUTH-001 (首次设置) — this endpoint is its prerequisite check