local: add PWA support for Android home screen install

Add app icons, update manifest with icon entries, and add app-shell
caching to service worker for offline/instant startup.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/web/public/index.html

@@ -6,6 +6,9 @@
   <meta name="description" content="Claude Code session manager with web interface">
   <meta name="theme-color" content="#0a0a0a">
   <meta name="google" content="notranslate">
+  <meta name="apple-mobile-web-app-capable" content="yes">
+  <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
+  <link rel="apple-touch-icon" href="icon-192.png">
   <link rel="manifest" href="manifest.json">
   <title>Codeman</title>
   <link rel="icon" type="image/svg+xml" href="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 32 32'%3E%3Cdefs%3E%3ClinearGradient id='g' x1='0%25' y1='0%25' x2='100%25' y2='100%25'%3E%3Cstop offset='0%25' stop-color='%2360a5fa'/%3E%3Cstop offset='100%25' stop-color='%233b82f6'/%3E%3C/linearGradient%3E%3C/defs%3E%3Crect width='32' height='32' rx='6' fill='%230a0a0a'/%3E%3Cpath d='M18 4L8 18h6l-2 10 10-14h-6z' fill='url(%23g)'/%3E%3C/svg%3E">