refactor(auth): rename AuthStatusCheckSubmitted → AuthInit (init-only)

The previous event name implied "re-check status", but the actual
semantics is just "read storage on app start and sync loginStatus into
the machine". It was being dispatched from three sites:

1. AuthStatusChecker mount useEffect (the legit one-time init)
2. AuthStatusChecker loginStatus-watching useEffect (dead code — the
   machine's onDone already writes loginStatus, re-reading storage
   just returns the same value as a no-op)
3. Sidebar post-logout effect (also dead code — AuthReset directly
   sets loginStatus to initialState's "notLoggedIn", and
   userLogoutActor already cleared storage, so the values are
   already aligned)

This commit:

- Renames event AuthStatusCheckSubmitted → AuthInit in:
  * auth-events.ts (type union)
  * auth-machine.ts (handler + transition target: checkingAuthStatus →
    initializing, mirroring UserInit / initializing in user-machine)
  * auth-status-checker.tsx (single dispatch site)
  * root-providers.tsx (one comment)

- Simplifies auth-status-checker.tsx from 74 → ~40 lines:
  * Removes useEffect ② (loginStatus-watching re-check)
  * Removes prevLoginStatusRef + skipNextChangeRef + useAuthState
    (dead loop-guard machinery no longer needed)

- Removes the post-logout re-check dispatch from sidebar-screen.tsx:
  * AuthReset alone is sufficient — userLogoutActor cleared storage
    and AuthReset writes back initialState, so they match by
    construction. No re-verification needed.

Net: -44 lines, no behavior change for the happy paths (startup,
login, logout), one fewer source of false re-checks.

src/stores/auth/auth-events.ts

@@ -13,8 +13,8 @@ export type AuthEvent =
   | { type: "AuthModeChanged"; mode: AuthMode }
   | { type: "AuthFormCleared" }
   | { type: "AuthReset" }
-  /** 启动 / 恢复时检查登录态 —— 拿 deviceId → 查 token（不自动创建游客账号） */
-  | { type: "AuthStatusCheckSubmitted" }
+  /** App 启动时一次性派发 —— 读 storage 把 loginStatus 同步到状态机 */
+  | { type: "AuthInit" }
   /** 显式游客登录 —— splash 上点"游客模式"按钮触发（不自动） */
   | { type: "AuthGuestLoginSubmitted" }
   // 业务事件（提交）