Add the Install the app bottom sheet for mobile browsers

- New InstallSheet mounted in the root layout: appears ~1s after load on
  iOS/Android phones and tablets, over any screen including the key gate,
  with a dimmed backdrop. Never on desktop, never in standalone mode, and
  at most once per 7 days after a dismissal (localStorage).
- Platform/browser detection (lib/install.ts): iPhone/iPad incl. iPadOS
  reporting as Mac with touch, Android, Safari vs Chrome vs other vs
  in-app browsers, with step 1 adapted accordingly.
- iOS: numbered steps with chips (Safari, Share, ... , More, Add to Home
  Screen) and the accent Add pill. Android: captured beforeinstallprompt
  turns into a native Install button; fallback steps use Install app /
  Add to Home screen chips and an accent Install pill.
- Close via X, backdrop, Escape or swipe-down on the handle; the site is
  untouched afterwards. Anchored to 100dvh so browser toolbars never hide
  the last step; pb-safe respects the home indicator.
- Dark sheet by default; light only when the app theme was explicitly set
  to light. Settings gains a mobile-only Install app row that reopens it.
- The inline head script captures beforeinstallprompt before hydration and
  records appinstalled. Old InstallHint banner removed.
- Tests: new install-sheet suite (45 checks across iPhone Safari/Chrome/
  in-app, Android Chrome/Samsung, desktop, prompt path, dismissal, 7-day
  expiry, standalone, Settings row, both themes); pwa suite updated.

app/layout.tsx

@@ -1,5 +1,6 @@
 import type { Metadata, Viewport } from "next";
 
+import { InstallSheet } from "@/components/InstallSheet";
 import { ServiceWorkerRegistrar } from "@/components/ServiceWorkerRegistrar";
 import "./globals.css";
 
@@ -51,15 +52,26 @@ export const viewport: Viewport = {
 /** Applies the saved theme before paint to avoid a flash. */
 const themeScript = `(function(){try{var s=localStorage.getItem('freezmo.theme');var d=s?s==='dark':window.matchMedia('(prefers-color-scheme: dark)').matches;if(d)document.documentElement.classList.add('dark');}catch(e){}})();`;
 
+/**
+ * Captures Chrome's `beforeinstallprompt` (it can fire before React hydrates)
+ * and records an install so the prompt never comes back. Static, no user data.
+ */
+const installScript = `(function(){try{
+window.addEventListener('beforeinstallprompt',function(e){e.preventDefault();window.__freezmoInstallPrompt=e;window.dispatchEvent(new Event('freezmo:installprompt'));});
+window.addEventListener('appinstalled',function(){try{localStorage.setItem('freezmo.install.installed','1')}catch(e){}window.dispatchEvent(new Event('freezmo:installed'));});
+}catch(e){}})();`;
+
 export default function RootLayout({ children }: { children: React.ReactNode }) {
   return (
     <html lang="en" suppressHydrationWarning>
       <head>
         <script dangerouslySetInnerHTML={{ __html: themeScript }} />
+        <script dangerouslySetInnerHTML={{ __html: installScript }} />
       </head>
       <body className="min-h-full antialiased">
         <div className="app-backdrop" aria-hidden />
         {children}
+        <InstallSheet />
         <ServiceWorkerRegistrar />
       </body>
     </html>

app/page.tsx

@@ -1,6 +1,5 @@
 import { ApiKeyGate } from "@/components/ApiKeyGate";
 import { AppHeader } from "@/components/AppHeader";
-import { InstallHint } from "@/components/InstallHint";
 import { LibraryScreen } from "@/components/LibraryScreen";
 import { MobileSidebar, Sidebar, SidebarOffset } from "@/components/Sidebar";
 import { TabBar } from "@/components/TabBar";
@@ -15,9 +14,6 @@ export default function HomePage() {
         <main className="min-w-0 flex-1">
           <AppHeader />
           <div className="mx-auto w-full max-w-6xl px-4 pb-tabbar lg:px-10 lg:pb-16">
-            <div className="mb-6">
-              <InstallHint />
-            </div>
             <LibraryScreen />
           </div>
           <TabBar />