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/stores/auth/auth-context.tsx

@@ -55,11 +55,12 @@ export function AuthProvider({ children }: AuthProviderProps) {
       password: state.context.password,
       username: state.context.username,
       confirmPassword: state.context.confirmPassword,
-      // isLoading 覆盖邮箱登录 / 邮箱注册 / OAuth 跳转（NextAuth 重定向期间）
+      // isLoading 覆盖邮箱登录 / 邮箱注册 / OAuth 跳转（NextAuth 重定向期间）/ 显式游客登录
       isLoading:
         state.matches("loadingEmailLogin") ||
         state.matches("loadingEmailRegister") ||
-        state.matches("loadingOAuth"),
+        state.matches("loadingOAuth") ||
+        state.matches("loadingGuestLogin"),
       errorMessage: state.context.errorMessage,
       isSuccess: state.matches("success"),
       loginStatus: state.context.loginStatus,