feat(pwa): installable web app + landing web entry

Make the web SPA an installable PWA and surface it to users:

- manifest.webmanifest + an install-only service worker + 192/512/maskable
  icons (ui/public); PWA head tags in index.html; the .webmanifest MIME type
  registered in the gateway (the distroless image has no /etc/mime.types).
- Platform-adaptive install CTA (components/InstallApp.svelte + lib/pwa):
  one-tap on Chromium, manual Add-to-Home-Screen instructions on iOS Safari,
  hidden elsewhere / once installed / inside a Mini App. Shown under the
  logged-out login card and at the bottom of Settings.
- The landing gains a third entry linking /app/ (the brand tile), with a
  caption under all three (Telegram / VK / Веб-версия).

The service worker is navigation-only (network-first, cached-shell fallback);
hashed assets and the Connect stream are untouched. It exists to satisfy
Chromium's installability requirement and is the single growth point for a
future opt-in offline mode.

Tests: pwa.ts unit tests; a webui probe (manifest/sw.js content-type + the
SPA-fallback-to-HTML trap); e2e for the one-tap CTA, the iOS instructions
modal and the landing web entry. Docs: ARCHITECTURE §13, FUNCTIONAL (+ru),
gateway README.

ui/public/manifest.webmanifest

@@ -0,0 +1,17 @@
+{
+  "name": "Эрудит (Скрэббл)",
+  "short_name": "Эрудит",
+  "description": "Игра в слова «Эрудит» (Скрэббл): играйте с друзьями, случайным соперником или ИИ-роботом.",
+  "lang": "ru",
+  "dir": "ltr",
+  "start_url": ".",
+  "scope": ".",
+  "display": "standalone",
+  "background_color": "#f3f4f6",
+  "theme_color": "#f3f4f6",
+  "icons": [
+    { "src": "icon-192.png", "sizes": "192x192", "type": "image/png", "purpose": "any" },
+    { "src": "icon-512.png", "sizes": "512x512", "type": "image/png", "purpose": "any" },
+    { "src": "icon-maskable-512.png", "sizes": "512x512", "type": "image/png", "purpose": "maskable" }
+  ]
+}

ui/public/sw.js

@@ -0,0 +1,53 @@
+// Install-only service worker.
+//
+// Its sole job today is to satisfy Chromium's PWA installability requirement (a registered
+// service worker with a fetch handler) so the web app can be installed to the home screen /
+// desktop — notably on Android, where the manifest alone is not enough. It deliberately does
+// NOT cache assets or the Connect-RPC stream: only top-level navigations are handled,
+// network-first with a cached-shell fallback, so the live app, its immutable hashed assets and
+// the live event stream are never served stale.
+//
+// This is the single designated growth point for the planned offline mode (a Settings toggle,
+// default online — see docs/ARCHITECTURE.md). Extend the fetch router here; keep the same
+// /app/ scope; gate any real caching behind the toggle and coordinate updates with the boot
+// version guard.
+const SHELL = 'scrabble-shell-v1'; // bump only when the SW strategy itself changes.
+
+self.addEventListener('install', () => {
+  // No cached content to migrate carefully, so activate the new worker immediately.
+  self.skipWaiting();
+});
+
+self.addEventListener('activate', (event) => {
+  event.waitUntil(
+    (async () => {
+      const keys = await caches.keys();
+      await Promise.all(keys.filter((k) => k !== SHELL).map((k) => caches.delete(k)));
+      await self.clients.claim();
+    })(),
+  );
+});
+
+self.addEventListener('fetch', (event) => {
+  const req = event.request;
+  // Only top-level navigations are handled. Hashed assets and the Connect-RPC requests are
+  // left untouched (no respondWith -> the browser performs its default fetch), so the worker
+  // can never break the live stream or serve a stale immutable asset.
+  if (req.mode !== 'navigate') return;
+  event.respondWith(
+    (async () => {
+      try {
+        const res = await fetch(req);
+        const cache = await caches.open(SHELL);
+        // One shell entry regardless of the deep-link path: the hash router resolves the route
+        // client-side, so any offline navigation can be served the same cached shell.
+        cache.put('shell', res.clone());
+        return res;
+      } catch {
+        const cache = await caches.open(SHELL);
+        const cached = await cache.match('shell');
+        return cached ?? Response.error();
+      }
+    })(),
+  );
+});