fix(push): monochrome brain badge for the Android status bar

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

frontend/public/sw.js

@@ -7,7 +7,7 @@
 //   would hand it the old values), the cache only offline.
 // - API requests are never touched; offline data comes from the app's own cache (lib/offline.ts).
 // Raise VERSION when this file changes in a way that needs fresh caches.
-const VERSION = 'v4';
+const VERSION = 'v5';
 const SHELL_CACHE = `mindsift-shell-${VERSION}`;
 const ASSET_CACHE = `mindsift-assets-${VERSION}`;
 const MAX_ASSETS = 80;
@@ -22,6 +22,7 @@ const SHELL_URLS = [
   '/icon-192x192.png',
   '/icon-512x512.png',
   '/apple-touch-icon.png',
+  '/badge-96x96.png',
 ];
 
 self.addEventListener('install', (event) => {
@@ -194,7 +195,8 @@ self.addEventListener('push', (event) => {
     self.registration.showNotification(msg.title || 'MindSift', {
       body: msg.body || '',
       icon: '/icon-192x192.png',
-      badge: '/icon-192x192.png',
+      // Status bar icon: Android only uses the alpha channel, the full app icon became a plain square
+      badge: '/badge-96x96.png',
       tag: msg.tag || undefined,
       data: { url: msg.url || '/' },
     })