fix: PWA manifest was never linked, icons 404'd; add install prompt (v0.64.0)

layout.tsx pointed <link rel="manifest"> at /manifest.json, but the
actual generated route (app/manifest.ts) serves at
/manifest.webmanifest -- the manifest was silently never picked up.
Its icons also referenced icon-192.png/icon-512.png, which don't
exist (only the .svg versions do). Both together meant Chrome/Android
install eligibility was broken with no visible error.

Also adds apple-mobile-web-app meta tags + viewport-fit=cover for
iOS home-screen installs, and a dismissible install banner driven by
the standard beforeinstallprompt event (Chromium-only by spec).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

apps/web/app/manifest.ts

@@ -10,8 +10,8 @@ export default function manifest(): MetadataRoute.Manifest {
     background_color: "#ffffff",
     theme_color: "#18181b",
     icons: [
-      { src: "/icon-192.png", sizes: "192x192", type: "image/png" },
-      { src: "/icon-512.png", sizes: "512x512", type: "image/png" },
+      { src: "/icon-192.svg", sizes: "192x192", type: "image/svg+xml", purpose: "any" },
+      { src: "/icon-512.svg", sizes: "512x512", type: "image/svg+xml", purpose: "any" },
     ],
   };
 }