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