Stage 17 round 6 (#16-20): landing page, /app/ move, cache + stream fixes

Close out Stage 17 round 6:

- Landing page at / — one Vite build with two entries (index.html = game
  SPA, landing.html = a lightweight landing reusing the theme/i18n/
  aboutContent leaf modules, not the app store).
- Move the web game SPA to /app/; the Telegram Mini App stays at /telegram/
  (gateway webui.Handler(stripPrefix, indexName): landing at /, SPA at /app/
  + /telegram/). Per-language "Play in Telegram" link via new
  VITE_TELEGRAM_LINK_EN/_RU build vars (button hides when unset).
- Cache headers: hash-named /assets/* immutable, HTML shells no-cache (the
  go:embed zero modtime emitted no validators, so the client re-downloaded
  the whole bundle every launch).
- Live-stream 15s abort fix: an immediate heartbeat on open + a 10s default
  interval (the first tick at 15s raced the edge idle timeout -> reconnect
  storm).

PLAN/ARCHITECTURE(§13)/FUNCTIONAL(+ru)/gateway+ui+deploy READMEs updated;
round 6 closed. Tests: gateway webui/connectsrv units, ui landing unit + e2e,
full e2e (60) green.

docs/FUNCTIONAL.md

@@ -21,6 +21,9 @@ email, the statistics screen, and the in-game history viewer with GCG export.
 Settings also pick the board's bonus-label style (beginner / classic / none). A hint **lays the suggested tiles on the board** for the player to confirm and
 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 into the web app or the matching Telegram bot; the game itself runs at
+`/app/` (web) and `/telegram/` (the Telegram Mini App).
 
 ### Identity & sessions *(Stage 1 / 6 / 9 / 15)*
 A player arrives from a platform (Telegram first), via email login, or as an
@@ -83,7 +86,11 @@ the other player and the leaver keeps their score. In a game with three or four
 players the leaver's seat is dropped and the others play on, the game ending when a
 single active player remains; the disposition of the leaver's tiles (returned to
 the bag or removed from play) is chosen when the game is created, and the leaver's
-rack is never shown to the others.
+rack is never shown to the others. A player's **board composition is kept per game**:
+the rack arrangement and the tiles laid but not yet submitted are saved as they compose
+and restored on return (including on another device); a player may **arrange tiles during
+the opponent's turn**, but that draft is position-only — the score preview and submission
+stay available only on the player's own turn.
 
 ### Robot opponent *(Stage 5)*
 When auto-match finds no human within ten seconds, a robot opponent takes the empty