feat(pwa): installable app (Add to Home Screen) for Android + iOS

- manifest.json (standalone display, theme color, maskable icons 192/512).
- generated square icons + apple-touch-icon (180) from the logo.
- apple-mobile-web-app + theme-color meta in home.html.
- sw.js gets a no-op fetch handler so it meets installability criteria (still
  no caching). static.js serves .json/.webmanifest with correct MIME.
- Installing as a PWA also unlocks Web Push on iOS (Apple requires Add to Home Screen).
Build marker -> pwa1.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

server/public/sw.js

@@ -4,6 +4,10 @@
 // the background / frozen / closed, and to open the right chat when one is clicked.
 self.addEventListener('install', (e) => { self.skipWaiting(); });
 self.addEventListener('activate', (e) => { e.waitUntil(self.clients.claim()); });
+// No-op fetch handler: present only so the app meets PWA installability criteria. It never
+// calls respondWith(), so the browser performs its normal network fetch — NO caching, so this
+// can never serve a stale app.
+self.addEventListener('fetch', () => {});
 
 self.addEventListener('push', (event) => {
   let d = {};