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/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 />