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/src/lib/pwa.svelte.ts

@@ -0,0 +1,88 @@
+// Reactive PWA install runtime: captures the Chromium install prompt, tracks the installed
+// state, and registers the install-only service worker. The pure platform branching lives in
+// pwa.ts. Structured after the other reactive lib modules (app.svelte.ts, router.svelte.ts).
+
+import { isIosSafari, isStandalone, resolveInstallMode, type InstallMode } from './pwa';
+import { insideTelegram } from './telegram';
+import { insideVK } from './vk';
+
+/** inMiniApp reports whether the app runs inside a Telegram or VK Mini App webview, where a web
+ *  install makes no sense (the platform manages its own launcher). Kept here, out of the pure
+ *  pwa.ts, so that module stays free of app imports for the node unit tests. */
+function inMiniApp(): boolean {
+  return insideTelegram() || insideVK();
+}
+
+// beforeinstallprompt is a Chromium-only event, absent from the DOM lib types.
+interface BeforeInstallPromptEvent extends Event {
+  readonly userChoice: Promise<{ outcome: 'accepted' | 'dismissed'; platform: string }>;
+  prompt(): Promise<void>;
+}
+declare global {
+  interface WindowEventMap {
+    beforeinstallprompt: BeforeInstallPromptEvent;
+    appinstalled: Event;
+  }
+}
+
+// Not named `state` (a Svelte-check hazard: `$state` would then read as a store subscription).
+const install = $state<{ deferred: BeforeInstallPromptEvent | null; installed: boolean }>({
+  deferred: null,
+  installed: isStandalone(),
+});
+
+/**
+ * installMode is the reactive install-CTA mode for the current platform and any captured prompt.
+ * Read inside a component's markup / $derived so the CTA updates when a Chromium prompt arrives
+ * (beforeinstallprompt fires shortly after load) or the app is installed.
+ */
+export function installMode(): InstallMode {
+  return resolveInstallMode({
+    deferredAvailable: install.deferred !== null,
+    standalone: install.installed,
+    iosSafari: isIosSafari(),
+    inMiniApp: inMiniApp(),
+  });
+}
+
+/**
+ * initInstallListeners wires the Chromium install prompt and the installed event. Harmless on
+ * any platform — the events fire only in an installable browser — so it may run unconditionally
+ * at startup, early enough to catch a prompt that fires before the CTA mounts.
+ */
+export function initInstallListeners(): void {
+  if (typeof window === 'undefined') return;
+  window.addEventListener('beforeinstallprompt', (e) => {
+    // Suppress Chromium's mini-infobar; the app presents its own CTA instead.
+    e.preventDefault();
+    install.deferred = e;
+  });
+  window.addEventListener('appinstalled', () => {
+    install.deferred = null;
+    install.installed = true;
+  });
+}
+
+/**
+ * promptInstall shows the native Chromium install dialog. It MUST be called directly from a user
+ * gesture (the deferred prompt is gesture-gated — no await before it). A deferred prompt is
+ * single-use, so it is cleared here; a no-op when nothing was captured.
+ */
+export async function promptInstall(): Promise<void> {
+  const deferred = install.deferred;
+  if (!deferred) return;
+  install.deferred = null;
+  await deferred.prompt();
+}
+
+/**
+ * registerServiceWorker registers the install-only worker (ui/public/sw.js). Web-only: skipped in
+ * the mock build (a real worker would perturb the Playwright run) and inside a Telegram/VK Mini
+ * App. Best-effort — a failed registration only means the app is not installable.
+ */
+export function registerServiceWorker(): void {
+  if (typeof navigator === 'undefined' || !('serviceWorker' in navigator)) return;
+  if (import.meta.env.MODE === 'mock') return;
+  if (inMiniApp()) return;
+  void navigator.serviceWorker.register('sw.js').catch(() => {});
+}