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-status-checker.tsx

@@ -1,74 +1,31 @@
 "use client";
 /**
- * AuthStatusChecker 启动 + 状态变化检查器
+ * AuthInit 派发器 —— App 启动时读 storage 同步 loginStatus 到状态机
  *
- * 触发时机：
- *   1. App 启动时（mount）派发一次 `AuthStatusCheckSubmitted`
- *   2. loginStatus 每次变化时（外部触发）也派发一次 —— 重新读 storage 校准
- *      例：OAuth sync 完成 → loginStatus 变 "facebook" → re-check 一次确认 storage 一致
- *          邮箱登录成功 → loginStatus 变 "email" → re-check 确认 token 已落盘
+ * 派发时机：仅 mount 时一次（`useEffect` deps = `[dispatch]`，永远不重跑）。
  *
- * 死循环防护（关键 —— 不加会无限递归）：
- *   - 状态机收 `AuthStatusCheckSubmitted` → 进 `checkingAuthStatus` → 读 storage → onDone 写回 loginStatus
- *   - 如果 useEffect 直接依赖 `loginStatus`，写回本身触发 effect → 再 dispatch → 死循环
- *   - 用 `skipNextChangeRef` 抑制一次：
- *       每次我们自己 dispatch 前把 flag 置 true；
- *       effect 见到 loginStatus 变化且 flag 为 true 时跳过并清 flag。
+ * 与原 `AuthStatusCheckSubmitted` 的区别：
+ *   - 原版本有两个 useEffect：① mount + ② loginStatus 变化 re-check
+ *   - re-check 是 dead code —— 状态机 onDone 已经把 loginStatus 写对，
+ *     再读 storage 只会拿到相同值（no-op），徒增死循环防护复杂度
+ *   - 新版本只保留 ①，命名 `AuthInit` 与 `UserInit` 对齐（user-machine 的同模式）
  *
  * 与 <OAuthSessionSync /> 平级：
- *   - AuthStatusChecker: 启动 + 状态变化时 re-check（"自己也能感知"）
- *   - OAuthSessionSync:   持续监听 NextAuth session（"别人也在写"）
+ *   - AuthStatusChecker: 启动时一次性 init（"自己启动时同步"）
+ *   - OAuthSessionSync:   持续监听 NextAuth session（"别人在写"）
  */
-import { useEffect, useRef } from "react";
+import { useEffect } from "react";
 
-import type { LoginStatus } from "@/models/auth/login-status";
-
-import { useAuthDispatch, useAuthState } from "./auth-context";
+import { useAuthDispatch } from "./auth-context";
 
 export function AuthStatusChecker() {
   const dispatch = useAuthDispatch();
-  const loginStatus = useAuthState().loginStatus;
 
-  // 上一次的 loginStatus（首次 mount 留 null —— 用来跳过首次 effect 跑）
-  const prevLoginStatusRef = useRef<LoginStatus | null>(null);
-  // 抑制下一次 loginStatus 变化触发的 effect（自己 dispatch 引起的写回要跳过）
-  const skipNextChangeRef = useRef(false);
-
-  // ─────────────────────────────────────────────────────────────
-  // ① App 启动时：派发一次
-  // ─────────────────────────────────────────────────────────────
   useEffect(() => {
-    console.log("[auth-status-checker] mount → dispatch AuthStatusCheckSubmitted");
-    skipNextChangeRef.current = true; // 抑制启动 check 写回 loginStatus 引起的 effect
-    dispatch({ type: "AuthStatusCheckSubmitted" });
+    console.log("[auth-init] mount → dispatch AuthInit");
+    dispatch({ type: "AuthInit" });
   }, [dispatch]);
 
-  // ─────────────────────────────────────────────────────────────
-  // ② loginStatus 变化时：派发一次（但跳过我们自己 check 写回的那次）
-  // ─────────────────────────────────────────────────────────────
-  useEffect(() => {
-    const prev = prevLoginStatusRef.current;
-    prevLoginStatusRef.current = loginStatus;
-    if (prev === null) return; // 首次 mount —— 启动那次由 ① 处理
-    if (prev === loginStatus) return; // loginStatus 没变 —— 不触发
-    if (skipNextChangeRef.current) {
-      // 这是我们自己 check 写回的 —— 抑制本次
-      skipNextChangeRef.current = false;
-      console.log(
-        "[auth-status-checker] loginStatus change suppressed (self-triggered)",
-        { from: prev, to: loginStatus },
-      );
-      return;
-    }
-    // 外部触发（OAuth sync / 邮箱登录 / 登出 等）的 loginStatus 变化 → 再 check 一次校准
-    skipNextChangeRef.current = true;
-    console.log(
-      "[auth-status-checker] loginStatus changed externally → re-check",
-      { from: prev, to: loginStatus },
-    );
-    dispatch({ type: "AuthStatusCheckSubmitted" });
-  }, [loginStatus, dispatch]);
-
   // 无 UI
   return null;
 }