refactor(splash): convert Skip to explicit guest login flow

- Splash Skip button now dispatches `AuthGuestLoginSubmitted` instead of
  direct routing, keeping guest auth under the state machine
- Update PWA install dialog copy ("Add to Home Screen") and drop favicon
  entry from manifest icons
- Add debug logging and routing sequence docs to splash-button

src/app/chat/components/pwa-install-dialog.tsx

@@ -9,8 +9,6 @@
  */
 import Image from "next/image";
 
-import { AppConstants } from "@/core/constants/app_constants";
-
 import styles from "./pwa-install-dialog.module.css";
 
 export interface PwaInstallDialogProps {
@@ -48,10 +46,10 @@ export function PwaInstallDialog({ onClose, onInstall }: PwaInstallDialogProps)
           priority
         />
         <h2 id="pwa-dialog-title" className={styles.title}>
-          Install {AppConstants.appTitle}
+          Add to Home Screen
         </h2>
         <p className={styles.content}>
-          {AppConstants.appTitle} can be installed on your device for a faster, full-screen experience.
+          Add CozSweet to Home Screen{"\n"}for the best experience
         </p>
         <div className={styles.actions}>
           <button

src/app/splash/components/splash-button.tsx

@@ -3,17 +3,21 @@
  * Splash 底部按钮组
  *
  * 原始 Dart: lib/ui/splash/widgets/splash_button.dart
- *   `Row(children: [Skip 文本, SizedBox 26, Facebook 登录按钮])`
+ *   `Row(children: [Skip 文本, SizedBox 26, 社交登录按钮])`
  *
  * 本组件是 splash 鉴权流程的**自治单元**：
  *   - 消费 `useSession()`（next-auth/react）监听 NextAuth session
  *   - 消费 `useAuthState` / `useAuthDispatch`（邮箱登录 + OAuth 流程统一收口到状态机）
  *   - 消费 `useChatDispatch` / `useUserDispatch`（登录成功后初始化）
  *   - 自管路由跳转（已登录 / 登录成功 → /chat）
- *   - Skip 用 `<Link>` 保留 SPA 体验
+ *   - **Skip 按钮 = 显式游客登录入口**（派发 `AuthGuestLoginSubmitted`，不是路由跳转）
  *   - 社交登录按钮仅派发 `AuthFacebookLoginSubmitted` 事件，由状态机负责调 NextAuth
+ *
+ * 跳转时序：
+ *   1. 派发事件（如 `AuthGuestLoginSubmitted`）
+ *   2. auth machine 进 loading state → API 调用 → onDone → state.isSuccess = true
+ *   3. useEffect 监听到 isSuccess → 调 chat/user store 初始化 + router.replace("/chat")
  */
-import Link from "next/link";
 import { useRouter } from "next/navigation";
 import { useEffect, useRef } from "react";
 
@@ -41,16 +45,28 @@ export function SplashButton() {
   const router = useRouter();
   const wasSuccess = useRef(false);
 
-  // 邮箱登录成功跳 /chat + 通知 chat/user 初始化
+  // 邮箱/OAuth/游客登录成功跳 /chat + 通知 chat/user 初始化
   useEffect(() => {
+    // DEBUG：isSuccess 状态透明化
+    console.log("[splash-button] useEffect state.isSuccess", {
+      isSuccess: state.isSuccess,
+      wasSuccess: wasSuccess.current,
+      willRedirect: state.isSuccess && !wasSuccess.current,
+    });
     if (state.isSuccess && !wasSuccess.current) {
       wasSuccess.current = true;
       chatDispatch({ type: "ChatAuthStatusChanged" });
       userDispatch({ type: "UserInit" });
+      console.log("[splash-button] useEffect → router.replace(/chat) [via isSuccess]");
       router.replace(ROUTES.chat);
     }
   }, [state.isSuccess, chatDispatch, userDispatch, router]);
 
+  // Skip = 显式游客登录入口（"以游客身份继续"）
+  const handleSkip = () => {
+    authDispatch({ type: "AuthGuestLoginSubmitted" });
+  };
+
   const handleFacebookLogin = () => {
     authDispatch({
       type: "AuthFacebookLoginSubmitted",
@@ -60,16 +76,19 @@ export function SplashButton() {
 
   return (
     <div className={styles.wrapper}>
-      {/* Skip 文本链接（next/link 渲染为 <a>，保留 SPA 体验） */}
-      <Link
-        href={ROUTES.chat}
+      {/* Skip 按钮 = 显式游客登录入口（派发 AuthGuestLoginSubmitted，**不**做路由跳转） */}
+      <button
+        type="button"
+        onClick={handleSkip}
+        disabled={isLoading}
         className={styles.skip}
-        aria-disabled={isLoading}
-        tabIndex={isLoading ? -1 : 0}
-        style={isLoading ? { pointerEvents: "none", opacity: 0.5 } : undefined}
       >
-        Skip
-      </Link>
+        {isLoading ? (
+          <LoadingIndicator color="#ffffff" />
+        ) : (
+          "Skip"
+        )}
+      </button>
 
       <div className={styles.separator} aria-hidden="true" />
 

src/app/splash/components/splash-screen.tsx

@@ -1,4 +1,11 @@
+"use client";
+
+import { useEffect } from "react";
+import { useRouter } from "next/navigation";
+
 import { MobileShell } from "@/app/_components/core/mobile-shell";
+import { AuthStorage } from "@/data/storage/auth/auth_storage";
+import { ROUTES } from "@/router/routes";
 
 import { SplashBackground } from "./splash-background";
 import { SplashLogo } from "./splash-logo";
@@ -7,6 +14,49 @@ import { SplashButton } from "./splash-button";
 import styles from "./splash-screen.module.css";
 
 export function SplashScreen() {
+  const router = useRouter();
+
+  // 启动时检查 localStorage 里的 token：
+  //   - loginToken（OAuth/email sync 写下的）→ 视为"已登录"跳 /chat
+  //   - guestToken（用户**显式**走"游客模式"留下的）→ 同样视为"已登录"跳 /chat
+  //   - 都没有 → 留在 splash（**不**自动创建游客账号 —— 见 auth-machine.ts 的 checkAuthStatusActor）
+  //
+  // proxy 读不到 localStorage（Edge runtime），所以这条 fallback 必须在 Client 侧。
+  //
+  // DEBUG：client 端**不**用 Logger（pino 引入会爆 client bundle），改用 console.log
+  //   临时调试，bug 修完即删。
+  useEffect(() => {
+    let cancelled = false;
+    void (async () => {
+      const storage = AuthStorage.getInstance();
+      // 用 getXxxToken() 拿 string | null（不是 hasXxxToken() 拿 boolean）
+      const [loginR, guestR] = await Promise.all([
+        storage.getLoginToken(),
+        storage.getGuestToken(),
+      ]);
+      const loginTok = loginR.success ? loginR.data : null;
+      const guestTok = guestR.success ? guestR.data : null;
+      const hasAny =
+        (loginTok != null && loginTok.length > 0) ||
+        (guestTok != null && guestTok.length > 0);
+
+      console.log("[splash] useEffect token check", {
+        loginToken: loginTok ? `${loginTok.slice(0, 8)}...` : null,
+        guestToken: guestTok ? `${guestTok.slice(0, 8)}...` : null,
+        hasAny,
+        willRedirect: hasAny && !cancelled,
+      });
+
+      if (!cancelled && hasAny) {
+        console.log("[splash] useEffect → router.replace(/chat)");
+        router.replace(ROUTES.chat);
+      }
+    })();
+    return () => {
+      cancelled = true;
+    };
+  }, [router]);
+
   return (
     <MobileShell background="var(--color-sidebar-background)">
       <div className={styles.wrapper}>