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/components/InstallApp.svelte

@@ -0,0 +1,85 @@
+<script lang="ts">
+  import { t } from '../lib/i18n/index.svelte';
+  import { installMode, promptInstall } from '../lib/pwa.svelte';
+  import Modal from './Modal.svelte';
+
+  // Platform-adaptive: 'oneTap' fires the native Chromium install dialog; 'iosInstructions' opens
+  // the manual Share -> Add-to-Home-Screen guide (iOS Safari has no programmatic install); 'hidden'
+  // renders nothing (already installed, inside a Telegram/VK Mini App, or an unsupported browser).
+  const mode = $derived(installMode());
+  let showIos = $state(false);
+
+  function onClick(): void {
+    // promptInstall must run synchronously from this gesture — the deferred prompt is gated on it.
+    if (mode === 'oneTap') void promptInstall();
+    else if (mode === 'iosInstructions') showIos = true;
+  }
+</script>
+
+{#if mode !== 'hidden'}
+  <button type="button" class="install" onclick={onClick}>
+    <img src="favicon.svg" alt="" width="40" height="40" />
+    <span class="text">
+      <span class="title">{t('install.title')}</span>
+      <span class="subtitle">{t('install.subtitle')}</span>
+    </span>
+  </button>
+{/if}
+
+{#if showIos}
+  <Modal title={t('install.iosTitle')} onclose={() => (showIos = false)}>
+    <ol class="steps">
+      <li>{t('install.iosStep1')}</li>
+      <li>{t('install.iosStep2')}</li>
+      <li>{t('install.iosStep3')}</li>
+    </ol>
+    <button type="button" class="ok" onclick={() => (showIos = false)}>{t('common.ok')}</button>
+  </Modal>
+{/if}
+
+<style>
+  .install {
+    display: flex;
+    align-items: center;
+    gap: 12px;
+    width: 100%;
+    text-align: left;
+    padding: 12px;
+    border: 1px solid var(--border);
+    border-radius: var(--radius-sm);
+    background: var(--surface);
+    color: var(--text);
+    cursor: pointer;
+  }
+  .install img {
+    flex: none;
+    border-radius: 8px;
+  }
+  .text {
+    display: flex;
+    flex-direction: column;
+    gap: 2px;
+    min-width: 0;
+  }
+  .title {
+    font-weight: 600;
+  }
+  .subtitle {
+    font-size: 0.85rem;
+    color: var(--text-muted);
+    line-height: 1.35;
+  }
+  .steps {
+    margin: 0 0 16px;
+    padding-left: 1.25rem;
+    line-height: 1.6;
+  }
+  .ok {
+    width: 100%;
+    padding: 10px 12px;
+    border: 1px solid var(--accent);
+    background: var(--accent);
+    color: var(--accent-text);
+    border-radius: var(--radius-sm);
+  }
+</style>