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/e2e/install.spec.ts

@@ -0,0 +1,59 @@
+import { expect, test } from './fixtures';
+
+// The install CTA (components/InstallApp.svelte) is platform-adaptive: a one-tap button where the
+// browser offers a beforeinstallprompt (Chromium), a manual instructions modal on iOS Safari, and
+// nothing elsewhere / once installed / inside a Mini App. The native OS install dialog is
+// browser-level and not drivable from Playwright, so these assert the CTA's presence and branch.
+
+const IPHONE_SAFARI =
+  'Mozilla/5.0 (iPhone; CPU iPhone OS 17_0 like Mac OS X) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/17.0 Mobile/15E148 Safari/604.1';
+
+test('web: a captured install prompt shows the one-tap CTA and clicking it prompts', async ({ page }) => {
+  await page.goto('/');
+  // The web login screen is shown (an ordinary browser tab, not a Mini App).
+  await expect(page.getByRole('button', { name: /guest/i })).toBeVisible();
+
+  // Hidden until the browser offers installation (Playwright never fires beforeinstallprompt).
+  await expect(page.getByRole('button', { name: /Install the app/i })).toHaveCount(0);
+
+  // Simulate Chromium offering the install: dispatch a beforeinstallprompt the app can capture.
+  await page.evaluate(() => {
+    const e = new Event('beforeinstallprompt') as Event & {
+      prompt?: () => Promise<void>;
+      userChoice?: Promise<unknown>;
+    };
+    (window as unknown as { __promptCalled: boolean }).__promptCalled = false;
+    e.prompt = () => {
+      (window as unknown as { __promptCalled: boolean }).__promptCalled = true;
+      return Promise.resolve();
+    };
+    e.userChoice = Promise.resolve({ outcome: 'accepted', platform: '' });
+    window.dispatchEvent(e);
+  });
+
+  const cta = page.getByRole('button', { name: /Install the app/i });
+  await expect(cta).toBeVisible();
+  await cta.click();
+  // Clicking calls the captured prompt (the native dialog itself is not observable here).
+  await expect
+    .poll(() => page.evaluate(() => (window as unknown as { __promptCalled: boolean }).__promptCalled))
+    .toBe(true);
+});
+
+test.describe('iOS Safari', () => {
+  test.use({ userAgent: IPHONE_SAFARI });
+
+  test('shows manual Add-to-Home-Screen instructions (no programmatic install)', async ({ page }) => {
+    await page.goto('/');
+    await expect(page.getByRole('button', { name: /guest/i })).toBeVisible();
+
+    // On iOS Safari the CTA shows at once (no beforeinstallprompt is ever fired there).
+    const cta = page.getByRole('button', { name: /Install the app/i });
+    await expect(cta).toBeVisible();
+    await cta.click();
+
+    // It opens the app's own instructions modal (not a native / Telegram popup).
+    await expect(page.getByRole('heading', { name: 'Add to Home Screen' })).toBeVisible();
+    await expect(page.getByText(/Tap the Share button/)).toBeVisible();
+  });
+});

ui/e2e/landing.spec.ts

@@ -46,3 +46,15 @@ test('the landing is a normal scrolling document (the SPA document-pin does not
   expect(state.shell).toBe(false);
   expect(state.bodyPosition).not.toBe('fixed');
 });
+
+// The web-version entry (/app/) is always present, alongside the build-var-gated Telegram/VK ones
+// (absent here, since e2e sets no VITE_* vars), each with a caption.
+test('the landing shows a web-version entry linking /app/, with a caption', async ({ page }) => {
+  await page.goto('/landing.html');
+  await expect(page.getByText(/Играй в «Эрудита»/)).toBeVisible(); // Russian by default
+
+  const web = page.getByRole('link', { name: 'Играть в браузере' });
+  await expect(web).toBeVisible();
+  expect(await web.getAttribute('href')).toContain('/app/');
+  await expect(page.getByText('Веб-версия')).toBeVisible();
+});