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.

docs/FUNCTIONAL.md

@@ -21,7 +21,8 @@ Settings also pick the board's bonus-label style (beginner / classic / none). A
 costs nothing when the rack has no legal move. The word-check accepts only the
 variant's alphabet, remembers answers within the session and rate-limits repeats.
 A public **landing page** at the site root introduces the game, switches language and
-theme, and links to the Telegram game channel and the VK Mini App; the game itself runs at
+theme, and links to the Telegram game channel, the VK Mini App and the **web version**
+(`/app/`) — each under a caption (Telegram / VK / Веб-версия); the game itself runs at
 `/app/` (web), `/telegram/` (the Telegram Mini App) and `/vk/` (the VK Mini App). The landing's theme is ephemeral
 (it follows the system scheme, not the saved preference); its language choice is saved. The
 landing always opens in **Russian** — the browser language is never auto-detected (crawlers
@@ -31,6 +32,11 @@ nondeterministic); a saved 🌐 choice still wins. The page carries a static Rus
 pinned to the production origin, JSON-LD, the favicon set and `robots.txt`), while the SPA
 shell is `noindex` — the landing is the only indexable page.
 
+On the plain web the client is an **installable PWA**: a logged-out player sees an install
+call-to-action under the login form (and at the bottom of Settings) that installs the app to the
+home screen / desktop in one tap where the browser supports it (Chromium), or shows manual
+Add-to-Home-Screen steps on iOS Safari; it is hidden once installed and inside the Mini Apps.
+
 ### First-run onboarding
 The first time a player opens the app it walks them through the interface with a light
 **coachmark overlay**: a dimmed layer draws one hint bubble at a time, each pointing — with a