feat(chat): limit in-game chat to one message per turn

Enforce one chat message per turn on both ends. The backend rejects a
second message in the same turn (ErrChatAlreadySentThisTurn -> 409
chat_already_sent), keyed on the move-driven turn start (turn_started_at).
The UI derives "already wrote this turn" from the message list against
GameView.lastActivityUnix (no counter, survives reopening, resets on turn
change), hides the field behind a short caption once the limit is reached,
and now reloads the game state on turn/game-state events so the toggle and
the limit follow the live game. Enter is gated on !busy to avoid a
double-send in the in-flight window.

Backend: new game.TurnStartedAt; social GameReader gains it; PostMessage
enforces the limit reusing lastMessageAt. UI: new lib/chatlimit.ts pure
logic + unit tests; Chat/ChatScreen wiring; chat.sentThisTurn and
error.chat_already_sent i18n (en/ru); extended chat e2e. Docs: FUNCTIONAL
(+ru), ARCHITECTURE, UI_DESIGN.

docs/ARCHITECTURE.md

@@ -444,7 +444,10 @@ English game the Latin pool.
 - **Chat**: per-game, persisted (kept with the game's archive), **≤ 60 runes**,
   and **validated on input** — links, email addresses and phone numbers (including
   lightly obfuscated forms) are rejected, since the chat is for quick reactions,
-  not contact exchange. Each message stores the sender's IP (forwarded by the
+  not contact exchange. Chat is allowed **only on the sender's own turn** and
+  **at most once per turn** (the turn boundary is the move-driven turn start; the
+  opponent's-turn control is the nudge); the backend enforces both and the client
+  mirrors them by hiding the field. Each message stores the sender's IP (forwarded by the
   gateway) for moderation. A sender who has disabled chat cannot post,
   and messages from a blocked sender are hidden from the viewer. The operator console
   has a **Messages** section that lists posted messages (nudges excluded)